The maximum height achieved by the projectile shot at an angle of 26° with the horizontal is 155.79 meters.
What is Projectile Motion?
Projectile motion is a form of motion experienced by an object or particle that is projected near earth's surface and moves along a curved path under the action of gravity only.
Given is a projectile projected towards a target a distance 1270 m away. Initial velocity of the projectile is 125.6 m/s and makes an angle 26° with the horizontal.
The vertical component of the initial velocity →
u[y] = 125.6 sin(26°) = 125.6 x 0.44 = 55.26 m/s.
The horizontal component of the initial velocity →
u[x] = 125.6 cos(26°) = 125.6 x 0.89 = 111.78 m/s
Horizontal distance covered →
h[x] = 1270 m
Time taken to travel the horizontal range →
t = h[x] / u[x]
t = 1270 / 111.78 = 11.36 seconds
The time at which the height is maximum →
t [max] = 11.36/2 = 5.68 s
Using Newton's second law of motion for vertical direction -
S[y] = u[y] t + 1/2 a[y] t²
At t = t [max], the vertical height will be maximum -
S[y] (max) = 55.26 x 5.68 - 1/2 x 9.8 x 5.68 x 5.8 =
S[y] (max) = 313.87 - 158.08
S[y] (max) = 155.79 meters.
Hence, the maximum height achieved by the projectile shot at an angle of 26° with the horizontal is 155.79 meters.
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A student drops a ball from the top of a 37-meter tall building. The ball leaves the student's hand with a zero speed. What is the speed of the ball at the moment just before it hits the ground?
Answer:
The ball accelerates because of gravity which is constant. So we can apply one of the equations of uniformly accelerated motion to solve the problem.
[tex]Vf^2=Vo^2+2aS\\[/tex] is compatible since [tex]S, Vo, a[/tex] are given enabling us to calculate [tex]Vf[/tex] .
[tex]Vf^2=(0m/s)^2+2*10m/s^2*37m\\Vf^2=20m/s^2*37m\\Vf^2=740m^2/s^2\\Vf=\sqrt{740} m/s\\ Vf=27.202941017 m/s\\[/tex]
A disc rotates about its axis at a constant rate. If the acceleration of the outer rim of the disc is 4.9 m/s2, and the period of the rotation is 2.0 s, what is the radius of the disc?
The radius of the disc will be 0.496 meters.
What is Angular velocity?The pace at which an object rotates or revolves around an axis is known as its angular velocity. The Greek letter omega stands for angular velocity. Because it is expressed as an angle per unit of time, angular velocity in the SI is measured in radians per second. [[tex]M^{0}L^{0}T^{-1}[/tex]] is the dimensional formula for angular velocity.
According to the question, the given values are :
Acceleration, a=4.9 m/s² and,
Period of rotation, T=2.0 seconds
So, angular velocity (ω) of disc =2π/T
⇒2π/2
= π rad/sec.
Acceleration= rω²
4.9= r×π²
r=0.496 meters.
Hence, the radius of the disc will be 0.496 meters.
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The Universal Gravitational constant
gives the mass and value a direction
converts the ratio of mass and distance to Newtons
gives the mass and distance a value
converts the ratio of mass and distance to kilograms
According to the given question, mBg- mAg = a(mA + mB) is the equation that will be used to determine acceleration.
The gravitational constant, represented by the capital G, is an empirical physical constant used in the calculation of gravitational effects in both Albert Einstein's theory of general relativity and Sir Isaac Newton's law of universal gravitation.
It is the proportionality constant in Newton's law that links the gravitational force between two bodies to the sum of their respective masses and the square root of their distance. It quantifies the relationship between the energy-momentum tensor and the spacetime geometry in the Einstein field equations.
The measured value of the constant is known to four significant digits with some certainty. Its value is approximately 6.674×10−11 m3⋅kg−1⋅s−2 in SI units.
Given in the qusetion
T - WA = mAa --------------1
WB - T = mBa --------------2
We know that, WA = mAg and WB = mBg
T = mAa + WA
T = mAa + mAg --------------3
Similarly, T = WB - mBa
T = mBg- mBa --------------4
From equation 3 and 4
mAa + mAg = mBg- mBa
mAa + mBa = mBg- mAg
a(mA + mB) = mBg- mAg
So, mBg- mAg = a(mA + mB) is the equation that will be used to determine the acceleration.
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Your question is incomplete. Please check the full content below.
The Universal Gravitational constant converts the ratio of mass and distance to Newton
gives the mass and distance a value
converts the ratio of mass and distance to kilograms
gives the mass and value a direction
The following equations are for two connected objects in the axis of motion
T-WA=mAa
WB-T=mBa
Which of the following equations would be used to determine the acceleration
T+mBg-mAg=(mA+mB)a
-T+mBg-mAg=(mA+mB)a
mBg-mAg=(mA+mB)a
mBg-mAg=mAa
A curve at a racetrack has a radius of 800 m and is banked at an angle of 7.0°. On a rainy day, the coefficient of friction between the cars' tires and the track is 0.50. What is the maximum speed at which a car could go around this curve without slipping?
The maximum speed at which a car could go around this curve without slipping is6.12m/s
To solve this it is necessary to take concepts related to Centripetal Force and Friction Force.
In the case of the centripetal force,
Fc = mv²/r ....1
Where,
m=mass
v= velocity
r= Radius
In the case of the Force of Friction we have to,
F= [tex]\mu[/tex]mg ......1.
Where,
[tex]\mu[/tex] = Friction Constant
m= mass
g= gravity
the centripetal equal to the friction force to stay on the road, in this way
mv²/r = [tex]\mu[/tex]mg
v² = mgr
v = √([tex]\mu[/tex]gr)
The coefficient of friction between the cars' tires and the track
[tex]\mu[/tex] = 0.50
radius = 800m
g = 9.8 m/s²
using above values we get
v = [tex]\sqrt[]{800*9.8*0.5}[/tex]
V = 6.12m/s
The maximum speed at which a car could go around this curve without slipping is6.12m/s
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What is measurement ?...
Answer:
the size, length, or amount of something, as established by measuring.
Consider the two vectors, A= 19.5x + 13.5y and B=3.4x - 4.5y.
What is the magnitude of the vector A - B?
What is the angle of the vector A - b, measured counterclockwise in degrees from the positive x-axis?
What is the magnitude of the vector 3A + B?
What is the angle of the vector 3A + B, measured counterclockwise in degrees from the positive x-axis?
The calculated angle is 305° and if v=a,b is the position vector, then |v|=a²+b² is the calculated magnitude.
If v=a,b is the position vector, then |v|=a²+b² will give the magnitude. Depending on the application, the direction is equal to the angle made with the x-axis or the y-axis. The formula tan=(ba)=tan1 determines the direction of a position vector (ba), We may say that the vector must be inclined in the fourth quadrant in this case because the vector's x and y components are both positive.
Consequently, the angle must be greater than 270 degrees and less than 360 degrees.
Now, in order to determine the value, we can say that
tanθ=opposite side/adjacent side
=8.6/6.1
=tan⁻¹1.41
=54.65, which indicates that it is inclined at an angle above with the X axis in the fourth quadrant (360-54.65 = 305.6°).
Consequently, the proper response will be 305° degrees if the angle is measured counterclockwise.
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At the beginning of a 3.0-h plane trip, you are traveling due north at 192 km/h. At the end, you are traveling 250 km/h in the northwest direction (45° west of north).
Find the magnitude of the change in velocity.
Find the change in direction of your velocity. Enter the angle in degrees where negative indicates north of west and positive indicates south of west.
What is the magnitude of your average acceleration during the trip?
The magnitude of the change in velocity is determined as 408.94 km/h.
The change in direction of the velocity is 64.4⁰ north of west.
The magnitude of the average acceleration during the trip is 0.0105 m/s².
Magnitude of change in velocityThe magnitude of change in velocity is the resultant velocity of the plane.
v² = a² + b² - 2ab cosθ
where;
θ is the angle between the two velocities = 45 + 90 = 135v² = (192²) + (250²) - 2(192 x 250) cos(135)
v² = 167,236
v = √167,236
v = 408.94 km/h
Vertical component of the velocityvyi = 192 km/h
vy2 = 250 x sin(45) = 176.77 km/h
vy(total) = 192 km/h + 176.77 km/h = 368.77 km/h
Horizontal component of the velocityvxi = 0
vx2 = - 250 km/h x cos(45) = -176.77 km/h
Change in direction of the velocityθ = arc tan (Vy/Vx)
θ = arc tan(368.77 / -176.77)
θ = -64.4 ⁰
θ = 64.4⁰ north of west.
Acceleration of the tripa = v/t
v = 408.94 km/h = 113.6 m/s
h = 3 h = 10,800 seconds
a = (113.6 m/s) / ( 10,800 s)
a = 0.0105 m/s²
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If the length of the pendulum in pendulum clock increases by 0.1 % , then the error in time per day is
a) 86.4s
b) 4.32s
c) 43.2s
d) 8.64s
JEE Mains 2022
When the length of the pendulum in pendulum clock increases by 0.1 % , then the error in time per day is c) 43.2s
How to calculate the time?Let the pendulum = L
The time in a day will be: = 60 × 60 × 24
When the length is increased, the new length will be:
= L + 0.001L
New time period will be:
T =✓0.001s
Now, the error in a day will be:
= ✓0.001 × 60 × 60 × 24 - 1 × 60 × 60 × 24.
= 60 × 60 × 24(✓1.001 - 1)
= 43.2 seconds.
Therefore, the correct option is C.
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2.Three sets of temperatures in Celsius, Fahrenheit and Kelvin scales respectively are given below. In which set do the thermometer scales show temperature of the same object? (a) 0°C, 32° F, 273 K (b) 0° C, 60° F, 373 K (c) 10° C, 32° F, 373 K
A 1900 kg car traveling at a speed of 14 m/s
skids to a halt on wet concrete where = 0.60.
How long are the skid marks?
The length of the skid marks is 136m.
Speed is the time charge at which an object is moving alongside a path, whilst pace is the price and direction of an item's movement. The rate of change of role of an item in any route. speed is measured because of the ratio of distance to the time in which the space changed into included.
calculation,
mass of car = 1900kg
speed = 14 m/s
F = ma
a = F(friction) / m
F(friction) = mu F(normal)
F(friction) = mu g m
a = mu g m / m
a = mu g
a = 0.6 * 9.81m/s²
a = 5.886 m/s²
v² = 2 a x
x = v² / 2 a
x = (40m/s)²/ 2 * 5.886m/s²
x = 136m
Speed is a way of measuring how quickly something is shifting or being executed, or something moving rapidly. Speed is described because of the charge of trade of distance with time. It has the dimension of distance by time. therefore, the SI unit of pace is given as the aggregate of the simple unit of distance and the primary unit of Time. for this reason, the SI unit of velocity is a meter in step 2d. the rate of a body is converting with appreciation to time it's far shifting with a non-uniform velocity.
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Interpreting Graphics
6. Figure 1.9 shows position-time graphs of the straight-line movement of
two brown bears in a wildlife preserve. Which bear has the greater aver-
age velocity over the entire period? Which bear has the greater velocity
at t = 8.0 min? Is the velocity of bear A always positive? Is the velocity of
bear B ever negative?
Answer:
Time difference = T1-T2 = D1/V1-D2/V2 = D ( 1/V1-1/V2)
Time difference = 5.5 min = 5.5*60=330 sec, V1 = .09 m/s, V2= 1.9 m/s
330 = D (1/.9 – 1/1.9)
330= D(1.11-.5263)
330=D(.585)
D= 330/.585 = 564.3 m
Explanation:
7. A tennis ball thrown horizontally from the top of a water tower lands 20.0 m from the base of the tower. If the tennis ball is initially thrown at a velocity of 10.0 m/s: (a) how long does it take the tennis ball to reach the ground? (b) how high is the water tower? (b) how far away was the golfer from the hole when he hit the ball? A championship goffer uses a nine iron to chip a shot right into the cup. If the golf ball is launched at a velocity of 20m / s at an angle of 60 deg above the horizontal: (a) how long was the ball in the air? (c) what maximum height did the ball reach?
Time taken by the tennis ball to reach the ground is 1.23 second, if the initial velocity is 10.0 m/s.
Velocity is the time price at which an object is transferring alongside a route, even as the pace is the fee and path of an item's motion. put some other manner, velocity is a scalar price, at the same time as velocity is a vector.
Speed is the speed at which something moves in a particular direction. for instance as the rate of a car traveling north on a motorway, or the rate a rocket travels after launching. In a scalar way, absolutely the value magnitude of the velocity vector is continually the velocity of the motion.
Speed is a vector expression of the displacement that an item or particle undergoes with appreciation to time. the standard unit of speed magnitude (also known as velocity ) is the meter consistent with 2nd (m/s).
The top of a water tower lands 20.0 m
initial velocity = 10.0 m/s
time required to reach the ground =
S = ut + 1/2 at²
20 = 10t + 5t²
t = 1.23 second
The water is at a height of 20 m.
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How can you categorize the hazard in the hospitality industry?
.Which term is described as a shelf of undersea land reaching a depth of about 200 meters (656 feet) and extending out from the shoreline?
A. guyots
B. deep-sea trenches
C. abyssal plains
D. continental shelf
Option D. continental shelf
Continental shelf is a part of a continent that is submerged under an area of relatively shallow water known as a shelf sea.
It is given in the question, that the shelf of undersea land reaches 200 meters and it also extends out from the shoreline. This condition is only possible when a structure is submerged, and such submerged region can only be called as continental shelf.
On the other hand guyots is a underwater volcanic mountain and deep-sea trenches are the the long narrow lowerings in the ocean floor with the depth upto 6000 meters. And abyssal plains are the underwater ocean floors which cannot be found at the depth of 200 meters.
Therefore continental shelf is used to described as a shelf of undersea land reaching a depth of about 200 meters (656 feet) and extending out from the shoreline.
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3. A cube of Brass (density = 8.74g/cm³) has a mass of 87.321 grams. Determine
the height of the cube in cm. And in inches (1.00in = 2.54cm)
A cube of brass is ((density = 8.74g/cm³) .The height of the cube after calculating the given details is 2.15443 cm.
WHAT IS DENSITY ?Due to differences in density, two identically sized cubes constructed of different materials will typically not weigh the same when compared when weighed. Additionally, it implies that a massive Styrofoam cube can have the same weight as a tiny lead cube. Platinum, lead, iron, and other dense materials are a few examples
CALCULATIONDensity = 8.74 g/cubic cm
mass = 87.321 gms
Density = mass / volume
volume = mass / density = 9.99096109 cubic cm ≈ 10 cubic cm
side of cube = ∛10 cm = 2.15443 cm
∴ height of cube = 2.15443 cm .
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A cheetah can run at a maximum speed
106 km/h and a gazelle can run at a maxi-
mum speed of 75.6 km/h.
If both animals are running at full speed,
with the gazelle 63.4 m ahead, how long before
the cheetah catches its prey?
Answer in units of s.
Answer:
Explanation:
We find the difference in speeds between the 2 animals
106 - 75.6 = 29.4 km/h
then we convert it to m/s by dividing it with 3.6
29.4 / 3.6 = 8.2 m/s
distance divided by speed equals time
63.4 / 8.2 = 7.7 seconds
What is water pollution
And they're causes in Florida
The description of water pollution and it's likely causes in Florida can be found below.
What is water pollution?Water pollution is the contamination of water, especially surface water, by sewage effluent, fertilizer runoff, industrial chemical discharge etc.
These contaminants are called pollutants and when released into a body of water can deteriorate water quality and hamper its usage by humans.
Water pollution in Florida or any other developed state/country of the world can be caused by the following:
spills or leaks from oil and chemical containers.waste effluent going into surface water drains removing too much water from surface waters and groundwater.run-off containing fertilisers and pesticides from farming into surface waters.Learn more about water pollution at: https://brainly.com/question/19920929
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Question 3 (1 point)
You are traveling up on an elevator to the 95th floor of the Hancock tower. As it
nears the 95th floor, your weight appears to be ?
You are traveling up on an elevator to the 95th floor of the Hancock tower. As it nears the 95th floor, your weight appears to be lighter.
Here is an exercise in thought. Consider a container with internally completely reflecting surfaces that is partially filled with light and located at sea level on Earth. The light will be somewhat gravitationally redshifted as it ascends, which will cause it to reflect at the top of the container with a little less momentum. Similar to how it will be blue shifted when travelling downward and give the container's bottom greater momentum. Weight is a quality of something that is subject to gravity. Light is drawn to objects with mass by gravity because it has energy. Since two photons (separate "pieces" of light, in a broad sense) have energy, I imagine they would be attracted to one another gravitationally. However, it would be really little.
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11 )Four forces of magnitude 10 N, 5 N, 4 N and 6 N act on an object in the directions North, West, East, and South respectively. Find the magnitude and direction of their resultant.
The magnitude and direction of resultant force is 4.12N and direction is 75.96degree
The combined force that affects a body in a different way is known as the resultant force. Typically, it uses a vector calculation to calculate.
F net = / (square root of F1 resultant + F2 resultant + F1F2 cos tita)/........(1)
For instance, if two forces are acting in the same direction, we add them together; if they are acting in opposition, we subtract them from one another.
When two forces are exerting pressure on a body at an angle of, the combined net force is 4N in the direction of North. In this case, the two forces are 10N and 6N, which are operating in opposing directions. Additionally, 5N and 4N are moving in the other direction, resulting in a net force of 1N moving westward from these two forces.
by substituting we get F net =4.12N
direction is = 4 / tan tita = 75.96 degree
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If a ball is thrown upward at a speed of 10 m/s, and it reaches a height of 5.1 meters, how long
will it be in the air total?
Answer:
t = 10/9.81 = 1.02s
Explanation:
the ball will be up in the air for 1.02 seconds
5. A ball is shot into the air with an unknown initial velocity. The ball reaches its highest point after 7 seconds, at which point it has traveled 40 meters into the air. What was its initial velocity?
4. A radiographic technique of 100mA at 1/4 s has been used. If one
changes to the 400 mA station, the appropriate exposure time for the
same mAs is:
awnser D. 1600 mA
Explanation:
Ns/Np=Ip/Is
current is inverse
100/800=200/x
100x=160000
x=1600
Recording a change in which of the following would be an
example of a qualitative observation?
a velocity
b color
c force
d power
Chec
Recording a change in color would be an example of a qualitative observation and is therefore denoted as option B.
What is Qualitative observation?This is referred to as the type of observation which is characterized by the use of our senses such as sight, smell etc while on the other hand quantitative observation has to do with measurement of different types of number variables and parameters
Color was chosen as the most appropriate choice because it doesn't deal with numbers and it can be felt with the use of our sense of smell which is present in the nose of individuals.
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The current flowing through a lamp is 1.5AIt is plugged into a 120 V outletWhat is the resistance of the lamp? Ω
Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.
What is the resistance of the lamp?Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.
V = IR
Where V is the voltage or potential difference, I is the current and R is the resistance.
Given the data in the question;
Current I = 1.5AVoltage V = 120VResistance R = ?Plug the given values into the equation above and solve for R.
V = IR
120 = 1.5 × R
R = 120/1.5
R = 80Ω
Given the flow of current and the voltage, the resistance of the lamp is 80 Ohms.
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Answer:
80 is the answer
Explanation:
A car is traveling due north at 23.6 m>s.
Find the velocity of the car after 7.10 s if its
acceleration is (a) 1.30 m>s2 due north, or
(b) 1.15 m>s2 due south.
A car is traveling due north at 23.6 m>s.
Find the velocity of the car after 7.10 s if its
acceleration is
The acceleration is known to be: a(t) = 1.7 m/s2.
We must integrate over time to obtain the velocity function, and the results are:
v(t) = (1.7m/s^2)
*t + v0
If we suppose that we begin at 23.6 m/s, then the initial velocity is: v0 = 23.6 m/s, where v0 is the beginning velocity.
The velocity formula is then: v(t) = (1.7m/s2).
*t + 23.6 m/s
We now seek to determine the value of t such that v(t) = 27.8 m/s.
Consequently, v(t) = 27.8 m/s = (1.7 m/s2)
*t + 23.6 m/s = (1.7 m/s2) 27.8 m/s - 23.6 m/s
t = 2.5 seconds when *t 4.2 m/s = (1.7 m/s/2)
At such acceleration, 2.5 seconds are required.
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Ilya and Anya each can run at a speed of 7.50 mph and walk at a speed of 3.50 mph . They set off together on a route of length 5.00 miles . Anya walks half of the distance and runs the other half, while Ilya walks half of the time and runs the other half.
- Find Anya's average speed. (express in miles per hour)
- How long does it take Ilya to cover the distance? (express in minutes)
- Now find Ilya's average speed. (express in miles per hour)
The correct answer is 54.6 min.
Running speed of Ilya and Anya is v_r=7.50 mi/hr
Walking speed of Ilya and Anya is v_w=3.50 mi/hr
Total length of the route is d=5.00 miles.
Total time taken by Anya to cover the distance is
[tex]t_A= d/2/v_r+ d/2/v_w[/tex]
[tex]t_A= d/2v_r + d/2v_w[/tex]
[tex]t_A=d/2 \times1/v_r +1/v_w[/tex]
[tex]t_A= d/2 \times v_r+v_w / v_rv_w[/tex]
[tex]t_A[/tex]= 5.00/2 × 7.50+3.50/7.50 × 3.50 hr
[tex]t_A[/tex]= 5.00/2 × 11/26.25 hr
[tex]t_A[/tex]= 55/52.5 hr
[tex]t_A[/tex]=1.05 hr
Therefore Anya will take 1.05 hr to cover the distance.
Average speed of Anya is
[tex]v_{avg} = d/t_A[/tex]
[tex]v_{avg}[/tex]= 5.00/1.05 mi/hr
[tex]v_{avg}[/tex] = 4.76 mi/hr
Therefore Anya's average speed is 4.76 mi/hr.
If total time taken by Ilya to cover the distance is t , then
([tex]v_r[/tex] × t/2+(v_w × t/2=d))
t/2 × ([tex]v_r+v_w[/tex])=d
t × ([tex]v_r+v_w[/tex])=2d
t = 2d/([tex]v_r+v_w[/tex])
t = 2 × 5.00/7.50+3.50
t = 10/11 hr
t = 0.91 × 60 min
t = 54.6 min
Therefore total time taken by Ilya to cover the distance is 54.6 min.
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Polio is a disease that can cause paralysis. Doctors treated patients with casts and braces, but the work of Elizabeth Kenny led to the use of hot baths and exercise to treat polio victims. These patients had less incidence of paralysis. Kenny’s ideas and their acceptance were due to
Kenny’s ideas and their acceptance were due to open-mindedness because she led to the use of hot baths and exercise to treat polio victims.
Who was Elizabeth Kenny?Elizabeth Kenny was a world-renowned nurse from Australia who develop a treatment for poliomyelitis, a very serious viral disease caused by poliovirus.
Elizabeth Kenny's ideas were controversial because they may be considered to be against conventional medical treatments.
In conclusion, Kenny’s ideas and their acceptance were due to open-mindedness because she led to the use of hot baths and exercise to treat polio victims.
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What is the neutralizing reaction, and why is neutralization important?
A neutralization reaction is when an acid and a base react to form water and a salt and involves the combination of H+ ions and OH- ions to generate water.
Velocity in x direction
Initial velocity in y direction
Answer: Vx= 86.6 m/s & Vy= 50 m/s
Explanation:
Vx= 100*cos30° = 86.6 m/s
Vy= 100*sin30° = 50 m/s
When using
association to
store and
remember
information,
you are also
A. neural
networking
B. encoding
C. duplicating
When using association to store and remember information, you are also encoding.
When trying to store and remember information, the following stages take place in order:
EncodingStorageRetrievalStoring a memory trace is called as encoding. Perception leaves representation in memory. It is the conversion of information for storage purposes.
Therefore, when using association to store and remember information, you are also encoding.
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