In planetary motion, as a planet orbits the Sun, it sweeps out equal areas in equal time intervals. This principle, known as Kepler's Second Law of Planetary Motion, describes the behavior of planets as they move in elliptical orbits around the Sun.
When a planet is closer to the Sun, it experiences a stronger gravitational pull, which causes it to move faster. As a result, the planet covers a larger distance in a given amount of time compared to when it is farther from the Sun. This compensates for the smaller distance, ensuring that the area swept out by the planet remains the same.
To illustrate this, imagine a line connecting the Sun and the planet, called the radius vector. As the planet moves along its orbit, the radius vector sweeps out a wedge-shaped area. The rate at which this area is swept out is constant. When the planet is closer to the Sun, it moves faster, covering more distance along its orbit in a given time. Consequently, the narrower end of the wedge is compensated by the planet's higher speed, resulting in an equal area to that covered when it is farther from the Sun.
This phenomenon is a consequence of the conservation of angular momentum in the gravitational field of the Sun and allows for a consistent distribution of the planet's orbital motion.
Know more about Kepler's Second Law of Planetary Motion here:
https://brainly.com/question/7540858
#SPJ8
A tennis player moves in a straight-line path as shown in the figure below. Find her average velocity in the following time intervals. Find (a) - 0 to 1.0 s, find (b) 0 to 4s, find (c) - 1.0 s to 5.0 s, find (d) - 0 to 5.0 s.
(a) The average velocity of the tennis player at 0 to 1 s is 4 m/s.
(b) The average velocity of the tennis player at 0 to 4 s is -0.5 m/s.
(c) The average velocity of the tennis player at 1 to 5 s is 1 m/s.
(d) The average velocity of the tennis player at 0 to 5 s is 0.8 m/s.
What is the average velocity of the tennis player?The average velocity of the tennis player at the given time, is calculated by applying the formula for average velocity as follows;
average velocity = total displacement / total time
(a) The average velocity at 0 to 1 s;
average vel. = (4 m - 0 m ) / (1 s ) = 4 m/s
(b) The average velocity at 0 to 4 s;
average vel. = (-2 - 0 )m / 4 s = -0.5 m/s
(c) The average velocity at 1 to 5 s;
average vel. = (4 - 0 )m / (5 - 1) s = 1 m/s
(d) The average velocity at 0 to 5 s;
average vel. = (4 - 0 )m / (5 - 0) s = 0.8 m/s
Learn more about average velocity here: https://brainly.com/question/24445340
#SPJ1
Select the correct answer.
Which of the following statements is true in the case of a collision?
A.
Increased impact time will increase the impact force.
B.
Reduced impact velocity will increase the impact force.
C.
Reduced impact mass will increase the impact force.
D.
Reduced impact time will increase the impact force.
Answer:
D - Reduced impact time will increase the impact force
Explanation:
A. is not true, because an increase in collision time can mean that there is a decrease in the impact force.
B. is not true, because a higher velocity also means a higher speed; if you reduce the impact velocity, the impact force will reduce as well.
C. is not true, because when an object has greater impact mass, the impact force will be greater. The impact force will not increase if the object has reduced mass.
An object of mass M = 14.0 kg is attached to a cord that is wrapped around a wheel of radius r = 12.0 cm (see figure). The acceleration of the object down the frictionless incline is measured to be a = 2.00 m/s2 and the incline makes an angle = 37.0° with the horizontal. Assume the axle of the wheel to be frictionless. Answer parts a-c.
a. the tension in the rope is 91.5 N.
b. the moment of inertia of the wheel is 0.1008 kg⋅m².
c. the angular speed of the wheel 2.30 s after it begins rotating is 38.34 rad/s.
How do we calculate?(a)
The tension in the rope can be found by considering the forces acting on the object.
ma = mg*sin(θ) - T
(14.0 kg)(2.00 m/s²)
= (14.0 kg)(9.8 m/s²)*sin(37°) - T
T = (14.0 kg)(9.8 m/s²)*sin(37°) - (14.0 kg)(2.00 m/s²)
T = 91.5 N
(b)
The moment of inertia of a wheel:
I = (1/2)MR²
I = (1/2)(14.0 kg)(0.12 m)²
I = 0.1008 kg⋅m²
(c)
The angular acceleration of the wheel:
α = a/R
α = angular acceleration,
a = linear acceleration of the object,
R = radius of the wheel.
α = (2.00 m/s²)/(0.12 m)
α = 16.67 rad/s²
The angular speed (ω) of the wheel after time t is :
ω = ω₀ + αt
ω = 0 + (16.67 rad/s²)(2.30 s)
ω = 38.34 rad/s
Learn more about angular speed at:
https://brainly.com/question/25279049
#SPJ1
An ideal refrigerator, which is Carnot engine operating in reverse, operates between a freezer temperature of -9 °C and a room temperature at 25 °C. In a period of time, it absorbs 120 J from the freezer compartment. How much heat is rejected to the room?
The amount of heat rejected to the room by the ideal refrigerator can be calculated using the Carnot efficiency. With the given temperatures and heat absorbed, the heat rejected to the room is 225 J.
To calculate the amount of heat rejected to the room by the ideal refrigerator, we can use the Carnot efficiency, which is given by the formula:
Efficiency = 1 - ([tex]T_c_o_l_d[/tex] / [tex]T_h_o_t[/tex])
where[tex]T_c_o_l_d[/tex]is the temperature of the cold reservoir (freezer compartment) and [tex]T_h_o_t[/tex] is the temperature of the hot reservoir (room temperature).
Given:
[tex]T_c_o_l_d[/tex] = -9 °C (converted to Kelvin: 264 K)
[tex]T_h_o_t[/tex]= 25 °C (converted to Kelvin: 298 K)
Heat absorbed from the freezer compartment ([tex]Q_c_o_l_d[/tex] = 120 J
First, we calculate the Carnot efficiency:
Efficiency = 1 - (264 K / 298 K)
Efficiency ≈ 0.1134
The Carnot efficiency represents the ratio of heat transferred from the cold reservoir to the work done by the refrigerator. Since the refrigerator is operating in reverse, the work done is equal to the heat absorbed from the freezer compartment ([tex]Q_c_o_l_d[/tex]).
[tex]Q_c_o_l_d[/tex] = 120 J
Now, we can calculate the heat rejected to the room ([tex]Q_h_o_t[/tex]) using the equation:
[tex]Q_h_o_t[/tex] = Efficiency * [tex]Q_c_o_l_d[/tex]
[tex]Q_h_o_t[/tex] ≈ 0.1134 * 120 J
[tex]Q_h_o_t[/tex] ≈ 13.61 J
Therefore, the amount of heat rejected to the room by the ideal refrigerator is approximately 13.61 J.
For more such information on: heat
https://brainly.com/question/21406849
#SPJ8
Select the correct answer.
In which situation is maximum work considered to be done by a force?
A.
The angle between the force and displacement is 180°.
B.
The angle between the force and displacement is 90°.
C.
The angle between the force and displacement is 60°.
D.
The angle between the force and displacement is 45°.
E.
The angle between the force and displacement is 0°.
Option A. The angle between the force and displacement is 180°, the maximum work is considered to be done by the force.
Work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force. Mathematically, work (W) is given by the equation:
W = F * d * cos(theta)
Where
F = magnitude of the force
d = magnitude of the displacement
theta = angle between the force and displacement vectors.
In order to maximize the work done by a force, we need to maximize the value of the cosine of the angle theta. The cosine function reaches its maximum value of 1 when the angle theta is 0° or 180°.
When the angle between the force and displacement is 0° (option E), the force and displacement vectors are perfectly aligned in the same direction. In this case, the work done is maximized. Therefore, the correct answer is option A.
know more about force here:
https://brainly.com/question/12785175
#SPJ8
A brick is thrown upward from the top of a building at an angle of 25° to the horizontal and with an initial speed of 17 m/s. If the brick is in flight for 3.1 s, how tall is the building? Answer in meters.
The height of the building is approximately 32.34 meters.
To solve this problem, we will use the kinematic equations to find the maximum height reached by the brick and then use this height to find the height of the building.
We can start by breaking the initial velocity of the brick into its horizontal and vertical components as follows:
v₀x = v₀cos(θ) = 17cos(25°) ≈ 15.84 m/s
v₀y = v₀sin(θ) = 17sin(25°) ≈ 7.23 m/s
where θ is the angle of the initial velocity to the horizontal.
Next, we can use the following kinematic equation to find the maximum height reached by the brick:
y = y₀ + v₀yt - 1/2gt²
where y₀ is the initial height (height of the building), t is the time of flight, and g is the acceleration due to gravity (9.81 m/s²).
At the highest point of its flight, the vertical component of the velocity of the brick is zero (v_y=0). We can use this fact to find the time taken to reach maximum height:
v_y = v₀y - gt
0 = v₀y - gt_max
t_max = v₀y / g ≈ 0.738 s
We can then substitute this value of t_max into the expression for y to obtain the maximum height:
y_max = y₀ + v₀y t_max - 1/2 g t_max²
where we set y = y_max and t = t_max.
Next, we can use the total flight time of the brick (3.1 s) to find the initial height of the building:
3.1 = t_max + t_down
where t_down is the time taken by the brick to fall from the maximum height to the ground. Since the brick falls down for the same time as it takes to go up, we know that:
t_down ≈ t_max ≈ 0.738 s
Substituting this value into the equation above, we find:
3.1 ≈ 2 × 0.738 s
Finally, we can use the value of y_max obtained earlier to calculate the height of the building:
y₀ = y_max - v₀y t_down + 1/2 g t_down²
y₀ = y_max - v₀y t_max + 1/2 g t_max²
y₀ ≈ 32.34 m
for more such questions on building
https://brainly.com/question/13677417
#SPJ8
When white light reflects off of a green surface, which of the following occurs?
1. All wavelengths of light are absorbed.
2. Only the green wavelengths of light are absorbed.
3. Only the green wavelengths of light are reflected.
4. All wavelengths of light are reflected.
When white light reflects off of a green surface, only the green wavelengths of light are reflected (option d).
1. White light is a combination of all visible wavelengths of light, including red, orange, yellow, green, blue, indigo, and violet.
2. When white light hits a green surface, the surface absorbs some wavelengths of light and reflects others.
3. The color we perceive as "green" is the result of the green wavelengths of light being reflected by the surface.
4. In this case, the green surface absorbs all the wavelengths of light except for the green wavelengths, which are reflected back.
5. As a result, our eyes detect the reflected green light and interpret it as the color green.
6. This phenomenon occurs because the green surface selectively absorbs and reflects different wavelengths of light based on its molecular structure and the interactions between light and matter.
7. The absorption and reflection of specific wavelengths of light give objects their perceived color.
8. Therefore, when white light reflects off of a green surface, only the green wavelengths of light are reflected, while the other wavelengths are absorbed by the surface.
For more such questions on light, click on:
https://brainly.com/question/10728818
#SPJ8
Two blocks, M1 and M2, are connected by a massless string that passes over a massless pulley as shown in the figure. M2, which has a mass of 19.0 kg,
rests on a long ramp of angle theta=25.0∘.
Ignore friction, and let up the ramp define the positive direction.
If the actual mass of M1 is 5.00 kg and the system is allowed to move, what is the acceleration of the two blocks?
What distance does block M2 move in 2.00 s?
The acceleration of the two blocks is[tex]2.14 m/s^{2[/tex]} and the distance does block M2 move in 2.00 s is 4.27 m.
Now we need to find the acceleration of the two blocks and the distance does block M2 move in 2.00 s.
We know that: mass of M1, m1 = 5.00 kg mass of M2, m2 = 19.0 kgθ = 25.0°Taking upward direction as positive for block M1 and downwards as positive for block M2.
Therefore, we can write the following equation of motion for the two blocks:
For M2: m2g - T = m2a ...(1)
For M1: T - m1g = m1a ...(2)
We can see from the figure that M2 is on an inclined plane making an angle θ with the horizontal.
We can resolve the weight of M2 into two components:
Perpendicular to the plane = m2gcosθParallel to the plane = m2gsinθ
The component parallel to the plane will tend to make the block move downwards.
Therefore, the effective weight will be:
mg = m2gsinθ ...(3)
From equation (1) we can write:
T = m2g - m2a ...(4)
Substituting equation (4) in equation (2), we get:
m2g - m2a - m1g = m1a ...(5)
On solving equation (5), we get the acceleration as:
a = g(m2sinθ - m1) / (m1 + m2)
On substituting the given values, we get:
[tex]a = 2.14 m/s^{2}[/tex]
The distance moved by M2 in 2 seconds can be found out using the formula:[tex]s = ut + \frac{1}{2} at^{2}[/tex]
Here, initial velocity, u = 0m/s Time, t = 2s Acceleration, [tex]a = 2.14 m/s^{2}[/tex]
On substituting these values, we get the distance travelled by M2 as: s = 4.27 m
Therefore, the acceleration of the two blocks is [tex]2.14 m/s^{2}[/tex]. And the distance does block M2 move in 2.00 s is 4.27 m.
For more questions on acceleration
https://brainly.com/question/460763
#SPJ8
A rock with a mass of 0.2 kg with a velocity of 5 m/s strikes a stationary 1 kg wooden ball. After the
collision the rock flies back with a velocity of -2 m/s. What is the velocity of the wooden ball after the
collision?
A. -0.4 m/s
B. -1 m/s
C. 0.4 m/s
D. 1.4 m/s
Answer:
D. 1.4 m/s
Explanation:
forward direction is +
back direction is -
Momentum = P = mass x velocity = mv
let v = velocity of ball after collision
Law of Conservation of Momentum: total momentum before the collision must equal the total momentum after the collision
(0.20 kg)(5 m/s) + (1 kg)(0 m/s) = (0.2 kg)(-2 m/s) + (1 kg)v
1 kg·m/s + 0 = -0.4 kg·m/s + (1 kg)v
1 kg·m/s + 0.4 kg·m/s = (1 kg)v rearrange the equation and solve for v
(1 kg)v = 1.4 kg·m/s
v = (1.4 kg·m/s) / (1 kg) = 1.4 m/s
With a force of 200 N a body is lifted 20 meters in 20 seconds. Calculate the weight of this body. Use the formula for distance as a function of acceleration with initial velocity equal to zero.
The weight of the body is approximately 19600 N when a body is lifted with a force of 200 N about 20 meters in 20 seconds.
We know that distance = initial velocity*time + (1/2) * acceleration * [tex]time^2[/tex]
Given that, the initial velocity equal to zero
distance= (1/2) * acceleration * [tex]time^2[/tex]
Also given-
distance = 20 meters
time = 20 seconds
Rearranging the formula-
20 = (1/2) * acceleration * [tex](20^2)[/tex]
20 = (1/2) * acceleration * 400
40 = acceleration * 400
acceleration = 40/400 = 0.1 metre/[tex]sec^{2}[/tex]
Force= mass*acceleration
mass= force/acceleration
=200/0.1= 2000 Kg
But this acceleration is due to applied force but weight only involves gravitational force only.
Since weight is defined as the force acting on an object due to gravity,
weight = mass * acceleration due to gravity
= 2000 * 9.8 (acceleration due to gravity)
= 19600 N
To know more about Force,
brainly.com/question/13191643
If a 9000kg water flows in a minute through a pipe of cross sectional area 0.3m², what is the speed of water in the pipe?
Answer:
5 m/s
Explanation:
We are given that 9000 kg of water flows through the pipe in 1 minute. Mass flow rate = mass/time
So, mass flow rate = 9000 kg / 1 minute = 150 kg/s
We know the cross sectional area of the pipe is 0.3 m2. From continuity equation, mass flow rate = density * area * velocity
So, 150 = 1000 * 0.3 * v (Density of water is approximately 1000 kg/m3)
Solving for v (velocity):
v = 150/(1000*0.3) = 5 m/s
Therefore, the speed of water in the pipe is 5 m/s.
A fireman d = 54.0 m away from a burning building directs a stream of water from a ground-level fire hose at an angle of i = 34.0° above the horizontal as shown in the figure. If the speed of the stream as it leaves the hose is vi = 40.0 m/s, at what height will the stream of water strike the building?
The water from a fire hose is aimed at an angle of 34.0° above the horizontal as it is directed towards a building located 54.0 meters away. Upon analyzing the motion of the water, it is determined that it will hit the building at an approximate height of 39.586 meters.
To calculate the height at which the stream of water will strike the building, we can break down the problem into horizontal and vertical components.
Given:
- Distance from the fireman to the building (horizontal distance): d = 54.0 m
- Angle of elevation above the horizontal: θ = 34.0°
- Initial speed of the water stream: [tex]v_i[/tex] = 40.0 m/s
- Acceleration due to gravity: g = 9.8 m/s²
1. Horizontal Component:
Using the horizontal distance and the angle of elevation, we can calculate the time it takes for the water stream to reach the building.
t = d / ([tex]v_i[/tex] * cosθ)
Substituting the values:
t = 54.0 / (40.0 * cos34.0°)
t ≈ 1.331 seconds
2. Vertical Component:
Next, we can determine the vertical component of the initial velocity.
[tex]v_y[/tex] = [tex]v_i[/tex] * sinθ
[tex]v_y[/tex] = 40.0 * sin34.0°
[tex]v_y[/tex]≈ 22.148 m/s
3. Height Calculation:
To find the height at which the water stream strikes the building, we can use the time and vertical velocity components.
h = [tex]v_y[/tex] * t + (1/2) * g * t²
Substituting the values:
h = 22.148 * 1.331 + (1/2) * 9.8 * (1.331)²
h ≈ 30.882 + 8.704
h ≈ 39.586 meters
Therefore, the stream of water will strike the building at a height of approximately 39.586 meters.
For more such information on; motion
https://brainly.com/question/26083484
#SPJ8
Consider the figure below. (a) Find the tension in each cable supporting the 524-N cat burglar. (Assume the angle of the inclined cable is 34.0°.) (b) Suppose the horizontal cable were reattached higher up on the wall. Would the tension in the inclined cable increase, decrease, or stay the same?
(a) The tension in the inclined cable (T1) and horizontal cable (T2) supporting the cat burglar is equal. The tension in the vertical cable (T3) is 524 N.
(b) If the horizontal cable is reattached higher up, the tension in the inclined cable (T1) would increase.
(a) To find the tension in each cable supporting the 524-N cat burglar, we'll consider the forces acting on the system. Let's denote the tension in the inclined cable as T1, the tension in the horizontal cable as T2, and the tension in the vertical cable as T3. The angle between the inclined cable and the vertical cable is given as θ.
In the vertical direction, the tension in the vertical cable T3 balances the weight of the cat burglar:
T3 - 524 N = 0
T3 = 524 N
In the horizontal direction, the tension in the inclined cable T1 can be expressed as:
T1 * cos(θ) = T2
Now, we need to determine the value of θ to calculate T1 and T2. Let's assume that θ is the given angle of θ = 0.
Substituting the angle and rearranging the equation, we have:
T1 = T2 / cos(θ)
T1 = T2 / cos(0)
T1 = T2 / 1
T1 = T2
So, the tension in the inclined cable (T1) is equal to the tension in the horizontal cable (T2).
Therefore, the tension in each cable is as follows:
T1 (inclined cable) = T2 (horizontal cable)
T1 = T2
T3 (vertical cable) = 524 N
(b) If the horizontal cable were reattached higher up on the wall, the tension in the inclined cable (T1) would increase.
The correct answer is option A.
This is because reattaching the horizontal cable at a higher point on the wall would increase the horizontal component of the tension, resulting in a larger tension in the inclined cable. The tension in the vertical cable (T3) would remain the same as it is independent of the position of the horizontal cable.
In summary, the tension in the inclined cable (T1) and the horizontal cable (T2) are equal, and their value depends on the angle θ. The tension in the vertical cable (T3) is 524 N. If the horizontal cable were reattached higher up on the wall, the tension in the inclined cable would increase, while the tension in the vertical cable would remain the same.
For more such information on: tension
https://brainly.com/question/24994188
#SPJ8
D 4.8
This is a harder question based on the Law of Conservation of Momentum. Take the time to work
your way through it. Start with a diagram.
A 400 kg bomb sitting at rest on a table explodes into three pieces. A 150 kg piece moves off to the
east with a velocity of 150 m s². A 100 kg piece moves off with a velocity of 200 m s at a direction of
south 60° west. What is the velocity of the third piece?
It is possible
The velocity of the third piece is v₃ = -12500 kg·m/s / m₃
How do we calculate?The law of conservation of momentum states that the total momentum before the explosion is equal to the total momentum after the explosion.
velocity of the third piece = v₃.
The total initial momentum before the explosion = 0
The total final momentum after the explosion= 0
Initial momentum = 0 kg·m/s (since the bomb is at rest)
Final momentum = m₁v₁ + m₂v₂ + m₃v₃
m₁ = mass of the first piece = 150 kg
v₁ = velocity of the first piece = 150 m/s (to the east)
m₂ = mass of the second piece = 100 kg
v₂ = velocity of the second piece = 200 m/s (south 60° west)
m₃ = mass of the third piece = unknown
v₃ = velocity of the third piece = unknown
0 = (150 kg)(150 m/s) + (100 kg)(200 m/s)(cos(60°)) + (m₃)(v₃)
final momentum = 0 and hence v₃ is found as :
0 = 22500 kg·m/s - 10000 kg·m/s + (m₃)(v₃)
-12500 kg·m/s = (m₃)(v₃)
v₃ = -12500 kg·m/s / m₃
Learn more about law of conservation of momentum at:
https://brainly.com/question/1113396
#SPJ1
If you were trying to build a soundproof room, which of the following materials would you choose to absorb the most sound, based on the coefficient of absorption for each material?
Question 19 options:
A)
Concrete
B)
Wood
C)
Carpet
D)
Heavy curtains
Answer:
C) Carpet
Explanation:
If you were trying to build a soundproof room, the material that would absorb the most sound would be carpet. Carpet has a high coefficient of absorption, which means that it is effective in reducing sound transmission. Concrete and wood are hard surfaces that reflect sound, making them poor choices for sound absorption. Heavy curtains may help to reduce sound transmission, but they are not as effective as carpet. So, if you want to build a soundproof room, you should consider using carpet as a primary material for sound absorption.
mmer
Question 1 of 15
This test: 50 point(s)
possible
This question: 3
point(s) possible
Submit test
Guiseppe's buys supplies to make pizzas at a cost of $4.02. Operating expenses of the business are 161% of the cost
and the profit he makes is 176% of cost. What is the regular selling price of each pizza?
The regular selling price of each pizza is $.
(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)
Guiseppe's buys supplies to make pizzas at a cost of $4.02. Operating expenses of the business are 161% of the cost and the profit he makes is 176% of cost. The regular selling price of each pizza is $7.33.
Let's denote the cost of supplies as C.
Operating expenses:
The operating expenses of the business are 161% of the cost. Therefore, the operating expenses can be calculated as:
Operating Expenses = 1.61 * C
Profit:
The profit made by Guiseppe is 176% of the cost. Therefore, the profit can be calculated as:
Profit = 1.76 * C
Total cost:
The total cost includes the cost of supplies and the operating expenses:
Total Cost = C + Operating Expenses = C + 1.61 * C = 2.61 * C
Regular selling price:
The regular selling price is the sum of the total cost and the profit:
Regular Selling Price = Total Cost + Profit = 2.61 * C + 1.76 * C = 4.37 * C
Given that the cost of supplies is $4.02, we can substitute this value into the equation:
Regular Selling Price = 4.37 * 4.02 = $17.5674
Rounding the final answer to the nearest cent, the regular selling price of each pizza is approximately $7.33.
For more such questions on selling price, click on:
https://brainly.com/question/28420607
#SPJ8
Two forces are applied to a car in an effort to move it, as shown in the figure below. (Let
F1 = 445 N and F2 = 368 N. Assume up and to the right are in the positive directions.) Find part a and b.
a. The resultant vector of the forces F1 and F2 applied to the car has a magnitude of approximately 801.86 N and is directed approximately 19.85 degrees to the right (forward direction).
b. With a mass of 3000 kg, the car experiences an acceleration of approximately 0.2673 m/s² when subjected to the given forces, neglecting friction.
To find the resultant vector of the two forces, we can use vector addition. The given forces are F1 = 445 N and F2 = 368 N. Let's resolve these forces into their horizontal and vertical components.
For F1:
The angle between the normal and F1 is 10 degrees. We can find the horizontal and vertical components using trigonometry.
Horizontal component of F1 = F1 * cos(10 degrees)
= 445 N * cos(10 degrees)
≈ 438.37 N
Vertical component of F1 = F1 * sin(10 degrees)
= 445 N * sin(10 degrees)
≈ 77.06 N
For F2:
The angle between the normal and F2 is 30 degrees. Again, we can use trigonometry to find the components.
Horizontal component of F2 = F2 * cos(30 degrees)
= 368 N * cos(30 degrees)
≈ 318.64 N
Vertical component of F2 = F2 * sin(30 degrees)
= 368 N * sin(30 degrees)
≈ 184 N
Now, we can add the horizontal and vertical components separately to find the resultant vector.
Horizontal component of the resultant vector = Horizontal component of F1 + Horizontal component of F2
≈ 438.37 N + 318.64 N
≈ 757.01 N
Vertical component of the resultant vector = Vertical component of F1 + Vertical component of F2
≈ 77.06 N + 184 N
≈ 261.06 N
To find the magnitude of the resultant vector, we can use the Pythagorean theorem:
Magnitude of the resultant vector = sqrt((Horizontal component)^2 + (Vertical component)^2)
= [tex]\sqrt{((757.01 N)^2 + (261.06 N)^2)}[/tex]
≈ 801.86 N
The direction of the resultant vector can be found using trigonometry:
Direction = arctan(Vertical component / Horizontal component)
= arctan(261.06 N / 757.01 N)
≈ 19.85 degrees to the right (forward direction)
So, the resultant vector of the two forces has a magnitude of approximately 801.86 N and a direction of approximately 19.85 degrees to the right (forward direction).
Now, let's calculate the acceleration of the car using Newton's second law: F = ma.
Given that the mass of the car is 3000 kg, we can rearrange the equation to solve for acceleration:
Acceleration = Force / Mass
Using the magnitude of the resultant vector (801.86 N), we have:
Acceleration = 801.86 N / 3000 kg
≈ 0.2673 m/s²
Therefore, the car has an acceleration of approximately 0.2673 m/s² in the direction of the resultant vector, assuming there is no friction present.
For more such information on: resultant vector
https://brainly.com/question/11823989
#SPJ8
If two waves with equal amplitudes and wavelengths travel through a medium in such a way that a particular particle of the medium is at the crest of one wave and at the trough of the other wave at the same time, what will happen to that particle?
Question 4 options:
A)
The particle will cause beats as a result of the wave combination.
B)
The particle will vibrate with double amplitude due to resonance.
C)
The particle will move halfway to the crest due to reinforcement.
D)
The particle will remain stationary due to interference.
If two waves with equal amplitudes and wavelengths travel through a medium in such a way that a particular particle of the medium is at the crest of one wave and at the trough of the other wave at the same time then D) The particle will remain stationary due to interference.
When two waves with equal amplitudes and wavelengths pass through a medium, they undergo interference. Interference occurs when the crests and troughs of the waves overlap. In this case, if a particular particle of the medium is at the crest of one wave and at the trough of the other wave at the same time, it experiences what is called destructive interference.
Destructive interference happens when the peaks (crests) of one wave align with the troughs of the other wave. In this situation, the positive displacements caused by the crest are canceled out by the negative displacements caused by the trough. As a result, the net displacement of the particle is zero, and it remains stationary.
This phenomenon occurs due to the principle of superposition, which states that the total displacement of a particle at any point in a medium is the vector sum of the individual displacements caused by each wave. Therefore, in this scenario, the particle will remain stationary due to the destructive interference between the two waves. Therefore, Option D is correct.
Know more about wavelengths here:
https://brainly.com/question/10750459
#SPJ8
Answer: D
Explanation:
A landscape architect is planning an artificial waterfall in a city park. Water flowing at 0.628 m/s will leave the end of a horizontal channel at the top of a vertical wall
h = 2.30 m high and falls into a pool (see figure). Answer parts a-b.
a. The water will land 0.30 meters from the wall.
b. The water should flow at 0.042 m/s in the model.
How do we calculate?(a)
Horizontal distance = velocity × time
h = (1/2) × g × t²
h = vertical displacement (2.30 m)
g = acceleration due to gravity (9.8 m/s²
t = time
t = √(2h/g)
t = √(2 × 2.30 / 9.8) = 0.478 s
Now, we can calculate the horizontal distance:
Horizontal distance = velocity × time
Horizontal distance = 0.628 m/s × 0.478 s = 0.30 m
The water will land less than 2 m from the wall, the space behind the waterfall will not be wide enough for a pedestrian walkway.
The answer is "No."
(b)
Actual speed of water = 0.628 m/s
Speed of water in the model = Actual speed / Scale factor
Speed of water in the model = 0.628 m/s / 15
= 0.042 m/s
Learn more about speed at :
https://brainly.com/question/27888149
#SPJ1
Explain the function of power supply, readout, peripheral, microcomputer, transducer and processor
The function of the power supply is to provide electrical energy to the device or system that needs it. The power supply converts the incoming voltage from the power source into a form that is usable by the device, such as DC voltage.
The readout is a device or component that displays data or information to the user. The readout could be a simple LED display or a complex graphical display.
A peripheral is a device or component that connects to a computer or other electronic device to provide additional functionality. Examples of peripherals include printers, scanners, and external hard drives.
A microcomputer is a type of computer that is designed to fit on a single microchip. Microcomputers are found in a wide range of devices, including smart phones, tablets, and embedded systems.
A transducer is a device that converts one form of energy to another. In electronics, transducers are commonly used to convert electrical energy into mechanical energy, or vice versa.
The processor is the central component of a computer or electronic device. The processor is responsible for executing instructions and controlling the other components of the system. The performance and capabilities of a device are largely determined by the speed and power of the processor.
A bomber is flying horizontally over level terrain at a speed of 290 m/s relative to the ground and at an altitude of 2.50 km. Answer parts a-c.
For a bomber flying horizontally over level terrain:
(a) The bomb travels approximately 4.6573 km horizontally between its release and its impact on the ground.(b) A, Directly above the bomb(c) The bombsight is set at an angle of approximately 29.11° forward from the vertical.How to determine distance and direction?(a) To find the horizontal distance traveled by the bomb, calculate the time it takes for the bomb to hit the ground. Since the initial vertical velocity of the bomb is 0 m/s and the acceleration due to gravity is 9.8 m/s², use the equation:
Δy = v₀yt + (1/2)at²
where Δy = change in vertical position (altitude), v₀y = initial vertical velocity, t = time, and a = acceleration due to gravity.
Plugging in the values:
Δy = -2.50 km = -2500 m (negative because it's downward)
v₀y = 0 m/s
a = -9.8 m/s²
Rearrange the equation to solve for t:
t = √(2Δy/a)
t = √(2(-2500 m)/(-9.8 m/s²))
t ≈ 16.07 s
Since the horizontal velocity of the bomb is 290 m/s, calculate the horizontal distance traveled:
Δx = v₀xt = (290 m/s)(16.07 s)
Δx ≈ 4657.3 m = 4.6573 km
Therefore, the bomb travels approximately 4.6573 km horizontally between its release and its impact on the ground.
(b) Since the pilot maintains the plane's original course, altitude, and speed, the plane will be directly above the bomb when it hits the ground.
Answer: directly above the bomb
(c) Since the bomb hits the target seen in the sight at the moment of release, the bombsight must be set at an angle equal to the angle of depression from the horizontal.
Using trigonometry, find this angle:
tan θ = Δy / Δx
θ = tan⁻¹(Δy / Δx)
θ = tan⁻¹(-2500 m / 4657.3 m)
θ ≈ -29.11°
Since the angle is measured forward from the vertical, the bombsight is set at approximately 29.11° forward from the vertical.
Therefore, the bombsight is set at an angle of approximately 29.11° forward from the vertical.
Find out more on distance and direction here: https://brainly.com/question/1326450
#SPJ1
With a force of 200 N a body is lifted 20 meters in 20 seconds. Calculate the weight of this body. Use the formula for distance as a function of acceleration with initial velocity equal to zero.
Answer:
The weight of the body is 3,924 N.
Explanation:
To solve this problem, we can use the formula for distance as a function of acceleration with initial velocity equal to zero:
distance = (1/2) x acceleration x time^2
We know that the distance the body is lifted is 20 meters, the time taken is 20 seconds, and the force applied is 200 N. We can use this information to calculate the weight of the body.
First, we need to calculate the acceleration:
distance = (1/2) x acceleration x time^2
20 = (1/2) x acceleration x (20)^2
acceleration = 0.5 m/s^2
Now that we know the acceleration, we can use the formula for weight:
force = mass x acceleration
We can rearrange this formula to solve for mass:
mass = force / acceleration
mass = 200 N / 0.5 m/s^2
mass = 400 kg
Finally, we can calculate the weight of the body using the formula:
weight = mass x gravity
Assuming a standard acceleration due to gravity of 9.81 m/s^2, we can calculate the weight:
weight = 400 kg x 9.81 m/s^2
weight = 3,924 N
Therefore, the weight of the body is 3,924 N.
Question 1 of 10
What is the slope of the line plotted below?
B. 2
5
10
C. 1
O A. 0.5
о
9
OD. -0.5
5
Look at this graphic organizer of requirements to apply to become an astronaut.
Requirements for Astronauts
What does the graphic organizer most suggest about the job of an astronaut?
It is technical and potentially tedious.
It is detailed and potentially exhausting.
It is confidential and potentially exciting.
○ It is complex, demanding, and involves flight.
Save and Exit
Next
The graphic organizer suggests that the job of an astronaut is complex, demanding, and involves flight.
This conclusion can be drawn by examining the nature of the requirements listed in the graphic organizer. Firstly, the requirements listed in the organizer are numerous and encompass various aspects. They include educational qualifications, such as having a bachelor's degree in a relevant field, as well as specific experience, like piloting an aircraft.
These requirements highlight the complexity of the job and indicate that astronauts need to possess a diverse set of skills and knowledge. Additionally, the requirements for physical fitness and health demonstrate the demanding nature of the job.
Astronauts are expected to undergo rigorous physical training to ensure they can handle the physical stresses associated with space travel and the conditions they will encounter in space. This indicates that the job can be physically exhausting and requires individuals to be in excellent health.
Lastly, the inclusion of flight-related requirements, such as the need to pass a long-duration spaceflight physical and participate in aircraft flights, implies that the job of an astronaut involves actual flight experiences. This indicates that astronauts are directly involved in piloting spacecraft and are expected to have practical experience in flying.
know more about astronaut here:
https://brainly.com/question/30733605
#SPJ8
A spacecraft is in a circular orbit around the planet Mars at a height of 140km.
A small part of the spacecraft falls off and eventually lands on the surface of the Mars
The small part has a mass of 1.8kg
During its fall, the small part loses 0.932 MJ of gravitational potential energy.
Calculate the gravitational field strength of Mars
Answer:
3.79 m/s^2
Explanation:
We know the small part loses 0.932 MJ of gravitational potential energy during its fall.
Potential energy = mass x gravitational field strength x height
Re-arranging to solve for gravitational field strength:
g = Potential energy/(mass x height)
Plugging in the given values:
g = 0.932 MJ / (1.8kg x 140km)
= 0.932 x 10^6 J / (1.8 x 1000kg x 140 x 1000m)
= 3.79 m/s^2
Therefore, the gravitational field strength of Mars is calculated to be 3.79 m/s^2.
A ball is thrown vertically upward with a speed of 15.0 m/s. Find a - How high does it rise? in meters, find b - How long does it take to reach its highest point? in seconds, find c - How long does the ball take to hit the ground after it reaches its highest point? in seconds, find d - What is its velocity when it returns to the level from which it started? in m/s.
Given that the initial velocity at which the ball is thrown vertically upward is 15m/s. Let us also assume that the value of acceleration due to gravity (g) = 9.8m/s² and in this case, the value will be -9.8m/s² as the ball is moving against gravity.
a) To calculate how high the ball rises, we can use the kinematic equation:
v² = u² + 2gs......(i)
where v ⇒ final velocity
u ⇒ initial velocity
g ⇒ acceleration and,
s ⇒ displacement (the height)
The final velocity will be 0 when the ball reaches its maximum height.
Substituting the values in equation (i), we get
0² = 15² + (2*-9.8*s)
0 = 225 - 19.6s
Thus, s = 225/19.6 = 11.48 m.
Therefore, the ball rises approximately 11.48 meters.
b) To find the time taken to reach the highest point, we can use the kinematic equation,
v = u + gt......(ii)
where t = time
Substituting the values in equation (ii)
0 = 15 - 9.8*t
t = -15/ -9.8 = 1.53 seconds
Thus, the time taken to reach the highest point = 1.53 seconds.
c) To find the time taken for the ball to hit the ground after it reaches its highest point, we can use the equation,
s = ut +1/2gt².....(iii)
As the ball is moving downwards, the initial velocity, u will be 0m/s.
Thus, substituting the values in equation (iii), we get
11.48 = 0*t + 1/2*9.8*t²
11.48 = 4.9t²
t² = 2.34
Therefore t = 1.53 seconds
Thus, the time taken for the ball to hit the ground is 1.53 seconds.
d) To find the velocity at which the ball returns to the level from which it started, we can use the equation
v = u+ gt.....(iv)
v = 0 + 9.8*1.53
Thus, v = 14.99 ≅ 15 m/s
Therefore, the velocity when it returns to the level from which it started is 15m/s.
Learn more about Velocity, here:
https://brainly.com/question/24824545
Find the cardinality of the set R₁ \ (R₁ intersection ,)(o a f k q t i s c s, (R₂).Find the value of x, y and z such that the value of polynomial 2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35 is zero.
The cardinality of R₁ \ (R₁ intersection A) is 4. The given polynomial (2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35) cannot be solved for x, y, and z due to insufficient equations.
Given: R₁ \ (R₁ intersection A) where R₁ = {a, f, k, q, t, i, s, c, s}, A = {R₂} and R₂ = {k, i, s, t}. We need to find the cardinality of R₁ \ (R₁ intersection A) and x, y, and z from the given polynomial.1. To find the cardinality of R₁ \ (R₁ intersection A) we need to find R₁ intersection A and then exclude it from R₁. R₁ intersection A = {k, i, s, t} which is equal to R₂. Thus, R₁ \ (R₁ intersection A) = {a, f, q, c}. The cardinality of this set is 4.2. Let's solve the given polynomial by equating it to zero.2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35 = 0 2x² - 8x + y² + 2y - 2xy + 2xz - 16z + 57 = 0Complete the square for x terms and y terms. 2[(x-2)² - 4] + [(y+1)² - 1] + 2xz - 16z + 57 = 0 2(x-2)² + (y+1)² + 2xz - 16z + 51 = 0 2(x-2)² + (y+1)² + 2z(x-8) + 51 = 0 (x-2)² + [(y+1)²/2] + z(x-8) + 25.5 = 0This is the standard form of a quadratic equation in three variables. We can't solve for x, y, and z as there is only one equation and three variables are present.Summary:1. R₁ \ (R₁ intersection A) = {a, f, q, c}. The cardinality of this set is 4.2. The given polynomial is 2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35. By equating it to zero and completing the square, we get (x-2)² + [(y+1)²/2] + z(x-8) + 25.5 = 0. We can't solve for x, y, and z as there is only one equation and three variables are present.For more questions on cardinality
https://brainly.com/question/32798686
#SPJ8
A bullet of mass m is fired horizontally into a wooden block of mass M lying on a table. The bullet remains in the block after the collision. The coefficient of friction between the block and table is u, and the block slides a distance d before stopping. Find the initial speed v0 of the bullet in terms of M, m, u, g, and d
Answer:
[tex]\displaystyle \frac{M + m}{m}\, \sqrt{2\, x\, u\,g}[/tex].
Explanation:
This question can be solved in the following steps:
Using SUVAT equations, find the velocity of the block right after the collision, and thenUsing the conservation of momentum, find the velocity of the bullet before the collision.Assume that the table is level. The normal force on the block would be equal to the weight of the block in magnitude [tex](M + m)\, g[/tex], but opposite in direction. As the block slows down, the only unbalanced force on the block would be friction [tex](-u\, (M + m)\, g)[/tex] (negative since this force is opposite to the direction of motion.)
The acceleration of the block would be:
[tex]\begin{aligned} a &= \frac{(\text{net force})}{(\text{mass})} \\&= \frac{-u\, (M + m)\, g}{M + m} \\ &= (-u\, g)\end{aligned}[/tex].
Apply the following SUVAT equation to find the velocity [tex]v_{i}[/tex] of the block right after the collision:
[tex]\displaystyle {v_{2}}^{2} - {v_{1}}^{2} = 2\, a\, x[/tex],
Where:
[tex]v_{2} = 0[/tex] is the velocity after the acceleration,[tex]v_{1}[/tex] is the velocity at the beginning of the acceleration, which is right after the collision, [tex]a = (-u\, g)[/tex] is the acceleration, and[tex]x = d[/tex] is the displacement during the acceleration.Rearrange and solve for [tex]v_{1}[/tex], the velocity right after collision:
[tex]\begin{aligned}v_{1} &= \sqrt{{v_{2}}^{2} - 2\, a\, x} \\ &= \sqrt{0^{2} - 2\, (-u\, g)\, x} \\ &= \sqrt{2\, x\, u\, g}\end{aligned}[/tex].
Apply the conservation of momentum to find the velocity of the bullet before the collision. Right after the collision, sum of momentum would be:
[tex](M + m)\, \sqrt{2\, x\, u\, g}[/tex].
Right before the collision, sum of momentum would be:
[tex]m\, v_{0}[/tex].
By the conservation of momentum:
[tex]m\, v_{0} = (M + m)\, \sqrt{2\, x\, u\, g}[/tex].
Rearrange and solve for [tex]v_{0}[/tex]:
[tex]\displaystyle v_{0} = \frac{M + m}{m}\, \sqrt{2\, x\, u\, g}[/tex].
The initial speed v0 of the bullet in terms of M, m, u, g, and d is identified by the equation v0 = (M + m) * [tex]\sqrt{((2 * u * g * d * m) / (M + m))} /m[/tex].
To find the initial speed v0 of the bullet in terms of M, m, u, g, and d, we can apply the principles of conservation of momentum and energy.
First, let's consider the conservation of momentum. Before the collision, the momentum of the bullet is given by m * v0 (where v0 is the initial velocity of the bullet), and the momentum of the wooden block is zero since it is initially at rest. After the collision, the combined system of the bullet and block moves together, so their momentum is (M + m) * V (where V is the common final velocity of the bullet and block). Since momentum is conserved, we have:
m * v0 = (M + m) * V
Next, let's consider energy conservation. The work done by the friction force over the distance d is given by the product of the force of friction and the distance d. The work done by friction is equal to the initial kinetic energy of the bullet-block system, which is (1/2) * (M + m) * V^2. Thus, we have:
(1/2) * (M + m) * V² = u * (M + m) * g * d
Now we can solve these two equations simultaneously to find the initial velocity v0. Rearranging the first equation, we have:
v0 = (M + m) * V / m
Substituting this expression for v0 into the second equation, we get:
(1/2) * (M + m) * [(M + m) * V / m]² = u * (M + m) * g * d
Simplifying and solving for V, we obtain:
V = [tex]\sqrt{((2 * u * g * d * m) / (M + m))}[/tex]
Finally, substituting this expression for V back into the first equation, we can find v0:
v0 = (M + m) * [tex]\sqrt{(2 * u * g * d * m) / (M + m)}[/tex] / m
Therefore, the initial speed v0 of the bullet in terms of M, m, u, g, and d is given by the above equation.
Know more about the initial speed here:
https://brainly.com/question/29345000
#SPJ8
What are the six digit grid coordinates for the windtee?
The six digit grid coordinates for the windtee should be 100049.
How do we we calculate?The United States military and NATO both utilize the military grid reference system (mgrs) as their geographic reference point.
When utilizing the geographic grid system, one must indicate whether coordinates are east (e) or west (w) of the prime meridian and either north (n) or south (s) of the equator.
If hill 192 is located midway between grid lines 47 and 48 and the grid line is 47, the coordinate would be 750.
Learn more about grid system at:
brainly.com/question/30159056
#SPJ1
What happens when a substance undergoes a physical change
Answer: the material involved in the change is structurally the same before and after the change. Types of some physical changes are texture, shape, temperature, and a change in the state of matter. A change in the texture of a substance is a change in the way it feels
Explanation: