The total leaf area a of a leafy plant scales with the total plant's mass m as a∝m3/4. Part a if you replace one large tree with two smaller trees, each with half the mass of the original tree, by what factor do you increase the total leaf area?

The acceleration of the ball at t = 1.5 sec is -10 m/s².

The height of the building is 16 m.

The ball will reach maximum height after 0.2 seconds.

The mass of the ball is 2 kg.

The ball is thrown vertically from upwards top of the building.

Let the velocity of the ball is v and the total time taken by the ball be t.

Now, the velocity of the ball as a function of t is given as:

v(t) = 2 - 10t

The acceleration can be obtained by differentiating the velocity with respect to time.

Therefore,

a = dv/dt

a = d/dt ( 2 - 10t )

a = - 10 m/s²

When t = 1.5 sec

The acceleration of the ball is - 10 m/s².

(b) The ball reaches the ground at t = 2.0 sec.

Now, velocity can be defined as the differentiation of velocity with respect to time.

v(t) = dx/dt

dx/dt = 2 - 10t

dx = 2 - 10t

Now integration the above equation for limits x = 0 to x and time t = 0 to t = 2sec as the balls reached the ground in 2 seconds.

Then,

∫dx = ₀∫² [ 2- 10t]dt

x = [2t]₀² - [10t²/2]₀²

x = 4 - 20

x = -16 m

Therefore, the height of the building is 16 m.

(c) The ball will reach the maximum height when the instantaneous velocity is zero.

v(t) = 2 - 10t

0 = 2 - 10t

t = 2/10 = 0.2 sec

The ball will reach maximum height after 0.2 seconds.

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The complete question is mentioned below:

A ball of mass 2.0kg is thrown vertically upward from the top of a building. the ball velocity v is given as a function of time t by the equation v(t)= 2-10t. the positive direction is upward. what is the ball acceleration at time t = 1.5 complete. (b) if the ball reaches the ground at t=2.0s what is the height of the building? (c) at what time does the ball reach a maximum height above the building?

The initial velocity will be zero since the car started from rest, and final velocity is 40 m/s.

acceleration: the rate at which the speed and direction of a moving object vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates. The car began at zero miles per hour, or at rest. It then continued to speed quickly. A vector measurement of the rate and direction of motion is what is meant by the term "velocity." Simply said, velocity is the rate of movement in a single direction. Velocity may be used to gauge both the speed of a rocket launching into space and the speed of a car traveling north o6n a busy freeway.

T= 12s

D=480 m

velocity= 480/12

velocity=40 m/s.

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The correct answer is tan C = 8/15.

Six trigonometric ratios, namely Sine, Cosecant, Tangent, Cosecant, and Secant, are defined for right triangles in mathematics. These trigonometric ratios are actual functions that connect a right-angled triangle's angle to the ratios of its two side lengths. Basic trigonometric functions like Sin and Cos can be used to determine how a right triangle is shaped. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are the six trigonometric ratios; they are sometimes known as Sin, Cos, Tan, Csc, Sec, and Cot. These can be represented in terms of the sides of a right-angled triangle given a particular angle, which is why they are known as ratios.

From the figure

[tex]$\tan A=\frac{\text { leg opposite } \angle A}{\text { leg adjacent to } \angle A}: \tan (\angle A C B)=\frac{\overline{A B}}{\overline{B C}}$[/tex]

Substitute [tex]$\overline{A B}=8, \overline{B C}=15$[/tex] into [tex]$\tan (\angle A C B)=\frac{\overline{A B}}{\overline{B C}}: \tan (\angle A C B)=\frac{8}{15}$[/tex]

Hence tan C = 8/15.

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There is no gain or loss in energy as it remains constant in the system in case of interference.

When two waves interact, either positively or negatively, there is no gain or loss in the system's energy, according to the principle of conservation of energy.

The distribution of energy in the system changes depending on the angle of superimposition during constructive interference, but the system's overall energy does not change and remains constant.

Although it may appear that waves are canceling each other out or losing energy in the event of destructive interference, energy is still present. There is no gain or loss of energy in the system even though the energy distribution may alter, the energy may be preserved, and the system's temperature may rise.

Hence Energy does neither gain nor lose in the presence of interference; it remains constant.

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When a window washer does not want to change her position but still her position got changes to range then the force acting on the window washer is an Unbalanced force because only an Unbalanced force can change the position.

Unbalanced forces are those acting on a body when the net force acting on the body is greater than zero. The body alters its state of motion when unbalanced forces act on it. Or, In other words, the net force acting on an object is unbalanced when it is moving at a variable speed. For instance, when an apple falls from a tree, it experiences an imbalanced force equal to its weight. A toy vehicle being pushed is an example of an imbalanced force, and the toy car begins to move as a result of the unbalanced force.

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3.56 km/s is the speed of a one-dimensional compressional wave moving along a thin copper rod.

At one end of the rod, a hard hammer strike is delivered. With a time interval of Δt between the two pulses, a listener at the other end of the rod hears the sound twice as it travels through the metal and the air.

The time interval is given by t = L/v.

The delay between pulses arrivals is:

Δt = L [(1/v(air)) - (1/v(copper))]

Now,

When the copper rod is swapped out for a different substance and the sound speed is measured as v(r).

The speed of air, v(air) = 343 m/s

Then,

L = [  Δt / (1/v(air)) - (1/v(r)) ]

L = [  Δt / (1/343) - (1/v(r)) ]

Here L is the length of the rod, Δt is in seconds and v(r) is the speed of sound in the rod.

The amount of time travel in the rod is now minimal as v(r) approaches infinity. As a result, the rod's length will be close to 343Δt, which is the distance that sound travels through the air during the delay.

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The marble travel from the top of the ramp is  56.25 m.

Ramp is can be understand in physics, such as the inclined planes, also referred to as ramps . That means,ramp is a type of simple machine which manipulate the direction and magnitude of a force. It is very useful machine by which we can understand the problems in mechenics .

We are given that,

The marble rolls down from the ramp in time = t = 5s

Acceleration of the marble due to gravity = a = 4.5 m/s²

Therefore , for getting the distance (s) of the marble which travelled from the top of the ramp by using the equation of motion i.e. given as,

s = ut + (1/2) at²

Here the marble released from thew rest at the top of the ramp so that initial velocity u = 0 , therefore after putting the value above equation can be written as,

s = (1/2)× 4.5 m/s²×5s × 5s

s = 56.25 m

Hence, the marble travel from the top of the ramp 56.25 m after 5 seconds.

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(a) The block does not move a bit.

(b) The force on the block from the wall is −(12N)i+(5.0N)j

(a)

To know that the block is going to move or not we are using the formula,

We compare f and μF₁

If

f<μF₁,

the block does not slide on the wall

but if

f>μF₁,

the block does slide.

We are given,

F= This is the applied force

F₁= This is the normal force of the wall on the block.

f=This is the force of friction.

mg= This is the force of gravity.

The horizontal component of Newton’s second law is,

F-F₁=0

So, F= F₁ = 12N

and

μ F₁ =(0.60)(12N)=7.2N.

The vertical component is,

f-mg=0

so, f=mg=5.0N.

From the above calculation we can get that,

f<μF₁,

So The block does not move a bit

(b)Since the block does not move,

f=5.0N.

F₁ = 12N

So, The force of the wall on the block is

F(wall) =−F₁ i + f j=−(12N)i+(5.0N)j

Therefore from the above calculation we can conclude that, The force on the block from the wall is −(12N)i+(5.0N)j

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Disclaimer: The question is incomplete in the portal here is the total question.

Question:

A 12N horizontal force pushes a block weighing 5.0 N against a vertical wall (Fig.). The coefficient of static friction between the wall and the block is 0.60, and the coefficient of kinetic friction is 0.40. Assume that the block is not moving initially. (a) Will the block move? (b) In unit-vector notation, what is the force on the block from the wall?

Answer: Both are correct.

Explanation: When eating, food undergoes both physical and chemical changes.

Answer: Both girls are correct.

Explanation: Your body system undergoes both physical and chemical change when you eat.

Average speed is the total distance travelled in total time taken. Here, the total distance covered by the football player is 58.6m ad the average speed is 7.76m/s therefore, the time taken will be 7.55 sec.

What is Average Speed?

Average Speed is the rate at which the total distance is covered by an individual. It can be calculated by the formula:

Average Speed = Total distance travelled by an object ÷ Total time taken

Average Speed = 7.76 m/s

Total distance travelled = 58.6 m

Hence, time taken to cover the distance can be calculated by dividing the distance covered by the object by Average Speed of the object:

Time taken = 58.6 m ÷ 7.76 m/s

Time taken = 7.55 sec

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Answer:

Charges B and C are negative

Explanation:

• We are certain of a law of magnetism that states "Field lines move from positive charge to negative charge"

[tex]{}[/tex]

Answer:

B and C are negative.

Explanation:

This is because according to the law of charges in electric field line it says that the lines forming the electric field move from the positive terminal to the negative terminal,hence making B and C be negative as the lines are moving into them.

λ=0.303m is behind the police car.

The frequency of the emission is [tex]f=1000\, \text{Hz}[/tex]

The police car is traveling at a speed of [tex]$v_s=+40.0 \frac{\mathrm{m}}{\mathrm{s}}$[/tex]

When the air is calm, the sound moves at a speed of [tex]$v=343 \frac{\mathrm{m}}{\mathrm{s}}$[/tex]

When travelling away from the source, the observer's (another car) speed is

[tex]$v_o=-30.0 \frac{\mathrm{m}}{\mathrm{s}}$[/tex]

(c) The sound's frequency is (for the observer at rest): in front of the police car.

[tex]f^{\prime}=\frac{v}{v-v_s} f[/tex]

consequently, the needed wavelength is:

[tex]\lambda=\frac{v}{f^{\prime}}=\frac{v}{\frac{v}{v-v_s} f}[/tex]

Rearranging and canceling v gives us:

[tex]\lambda=\frac{v-v_s}{f}=\frac{343 \frac{\mathrm{m}}{\mathrm{s}}-40 \frac{\mathrm{m}}{\mathrm{s}}}{1000 \mathrm{~Hz}}=0.303 \mathrm{~m}[/tex]

Hence, λ=0.303m  is behind the police car.

A waveform signal's wavelength is defined as the separation between two identical points (adjacent crests) in adjacent cycles as the signal travels through space or along a wire.

This length is typically specified in meters (m), centimeters (cm), or millimeters (mm) in wireless systems (mm).

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The distance the fighter travels is 8062.85 m

This is the length between two points.

To calculate the distance the fighter travel, we use the formula below.

Formula:

Where:

From the question,

Substitute these values into equation 1

Hence, the distance the fighter travels is 8062.85 m

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The average horizontal force applied on the gate from the lake water. will be 882.9 kN

Force is defined as the external agent applied to any object which tries to displace the body from one place to another or resist the body movement.

Given,

width of gate, W = 5 m

depth of the lake, h = 6 m

density of water = 1000 kg/m³

Atmospheric pressure = 101 kPa

Pressure at the bottom of the gate will be calculated as below:-

P = ρ g h

P = 1000 x 9.81 x 6

P = 58860 Pa

Now, Force acting on the plate is

F = ( 1 / 2)pwh

F = ( 1 / 2 ) x 58860 x 5 x 6

F = 882900 N

F = 882.9 k N

The average horizontal force applied on the gate from the lake water is equal to F = 882.9 kN

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The toy train that moves around a circular track, of radius 0.55 m, 10 complete times over 3 minutes has a speed of: 0.1919 m/s

To solve this problem the formulas and the procedures we will use are:

v = (2*π * r * n)/ t

Where:

Information about the problem:

By converting the time unit from (min)  to (s) we have:

t = 3 min * 60 s/1 min

t = 180 s

Applying the tangential velocity formula we get:

v = (2*π * r * n)/ t

v = (2* 3.1416 * 0.55 m * 10)/ 180 s

v = 0.1919 m/s

In physics is the length of arc traveled in each unit of time in uniform circular motion. It is expressed in units of distance per time (m/s), (km/h).

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Answer: First multiply the numbers you have! 45 x 128 = 5760 miles ! Hope this helps!~

The value of y for the line in the plane of the two wires along which the total magnetic field is zero is 0.1667 m below the upper wire .

It is given that force per unit length is 320μ N/m and one wire carries a current [tex](I_1)[/tex] of 20.0 A and is located along the line y= 0.500 m .

Putting above values in equation (1) , we get

[tex]320\times10^{-6}=\frac{4\pi \times10^{-7}\times20.0\times I_2}{2\pi \times0.500}\\\ \\320\times10^{-6}=\frac{4 \times10^{-5}\times I_2}{5}\\\\I_2=\frac{320\times10^{-6}\times5}{4 \times10^{-5}} \\\\I_2=40A[/tex]

Now the magnitude of the magnetic field at a distance "a" due to long current carrying is given by

           [tex]B=\frac{u_0I}{2\pi a}[/tex]

The direction of this magnetic field is given by the right-hand rule of thumb of holding the wire in the right hand, with the outstretched thumb pointing in  the  direction of current flow and the direction of curled fingers pointing in the direction of magnetic field circulation. of wire.

Hence, field due the wire has an outward direction from the top side of the wire to the bottom side of the wire. Thus, the field is added, above the upper wire comes out of the paper for two wires  and enters the paper below the lower wire.

Between the two wires, due to top wire magnetic field is in the paper and due to the bottom wire magnetic field is outside so it is subtracted. The magnetic field is zero here.

Let the resultant magnetic field is zero at a distance x below the upper wire and then magnitude of the field at this distance due to both field must be equal and opposite and is given by

[tex]B=\frac{u_0I_1}{2\pi x} -\frac{u_0I_1}{2\pi (r-x)} \\\\0=\frac{u_0I_1}{2\pi x} -\frac{u_0I_1}{2\pi (r-x)} \\\\\frac{u_0I_1}{2\pi x} =\frac{u_0I_1}{2\pi (r-x)} \\\\\frac{I_1}{x} =\frac{I_2}{r-x} \\\\\frac{20}{x} =\frac{40}{0.500-x} \\\\20(0.500-x)=40x\\\\10-20x=40x\\\\10=60x\\\\\x=\frac{10}{60} \\\\x=0.1667m[/tex]

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A) 42.7% is the energy efficiency of the device.

Energy efficiency is a measure of how much energy is wasted. There are several ways to save energy, especially thermal energy, and the rate at which it is lost needs to be slowed down. Energy efficiency is defined as requiring less energy to complete an activity or reach a goal. Homes, structures, and production facilities that use less energy to create their products also consume less energy to heat, cool, and run gadgets and appliances.

Energy efficiency is one of the most straightforward and cost-effective ways to halt global warming, reduce consumer energy costs, and increase the competitiveness of American businesses. Energy efficiency is also a key component in the decarbonization process to attain net-zero emissions of carbon dioxide.

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Since Sandi's observation is a biased one, we should be most concerned about the observer bias.

When a researcher's expectations, viewpoints, or prejudices affect what they see or record in a study, this is known as observer bias. It typically has an impact on studies when observers are aware of the research objectives or hypotheses.

Similarly in Sandi's case, she has already drawn conclusions and formed biases on MacDonald's customers. She already anticipates that they will be overweight. Thus, this will have an impact on her observations.

Therefore, in Sandi's case, observer bias should be our main concern.

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Option (B) many

According to the lesson, it can be said that many adults have some of the same problems with sleep that Bailey does.

Sleeplessness is one of the most common issues, every second adult or a teenager is facing now a days. Due to a lot of responsibilities, we end up having little time for sleep and this in turn affects our body functions.

Good sleep hygiene is often recommended to improve sleep quality, which  also helps in alleviating anxiety due to work load and responsibilities.

Answer is Option (B) many

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The calculated distance is 20 km.

Speed indicates how quickly something, or someone is moving. If you know how far something has traveled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. For instance, if a car drives 120 miles in 2 hours, we may calculate the speed as 120 x 2 = 60 miles per hour. The units for speed are determined by the units of distance and time.

Recognizing that the gap between the trains is closing at a constant rate of 20 km/h,

the total time that elapses before they crash is

t=(20km)/(20km/h)

=1.0h.

During this time, the bird travels a distance of

x=vt

=(20km/1.0h)

=20km.

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0.385c m/s is the speed of the ball relative to Ed.

A frame of reference is a set of reference points—geometric points whose positions are known mathematically and physically—that define the origin, orientation, and scale of an abstract coordinate system.

If a body does not continuously adjust its position in relation to its environment throughout the course of time, it is said to be at rest.

In the frame S', Dina and Owen are at rest.

The speed of the ball with respect to Owen, u =0.800c

The speed of the frame S' with respect to frame S,  v = 0.600c

Distance between Dina and Owen, L(p) = 1.8 × 10¹² m

Speed of light, c = 3 × 10⁸ m/s

Therefore, the velocity of the ball in relation to Ed is:

u' = (u-v) / 1-(uv/c²)

u' = (0.8c - 0.6c) / 1- [(0.8c)(0.6c)/c²]

u' = (0.8c - 0.6c) / 1- [(0.8)(0.6)]

u' = 0.3846c ≈ 0.385c

The speed of the ball with respect to Ed is 0.385c m/s.

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The elastic modulus of magnesium bar is 3.14 GPa.

We need to know about the modulus of elasticity to solve this problem. The elastic modulus of material can be measured by strain and stress. It can be determined as

B = σ / e

B = (F/A) / (ΔV/V)

where B is modulus of elasticity, σ is stress, e is strain, F is force, A is area, V is initial volume, ΔV is volume stretched.

From the question above, we know that:

F = 22000 N

A = 1cm x 1cm = 1 cm²

V = A x 10cm = 10 cm³

ΔV = (10.07-10) x A =0.07 cm³

Convert to SI unit

A = 1 x 10¯⁴ m²

V = 10¯⁵ m³

ΔV = 7 x 10¯⁴ m³

By substituting the following parameters, we get

B = (F/A) / (ΔV/V)

B = (22000 / (1 x 10¯⁴) / (7 x 10¯⁴ / 10¯⁵)

B = 3.14 x 10⁶ Pa

B = 3.14 GPa

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Rxpression for the electric field E at the center of the semicircle is

Q/[tex]\frac{}{}[/tex](2π² ∈₀ R²) (-j) , where j is the unit vector.

Since the total charge on the semicircle is Q and the Radius of the semicircle is  R.

if we consider that an elemental charge makes an angle theta with the horizontal on the semicircle and along the y axis the charge distribution is symmetrical, which means there is a symmetrical charge on the other side too.

So, the vertical component will get added and the horizontal component will cancel out each other .

No let consider  due to  elemental charge dE  be the electric Field and λ    be the charge per unit length .

So, we can write λ =Q/πR.

k = 1 /(4π∈₀)

Now the total Electric Field at the center is

= 2dE sinθ

= 2kλ/r [tex]\int\limits^_ {} \,[/tex] Sinθ dθ

After integrating the above term from 0 to π/2, we get

E= 2kλ / R (-j)

E=Q/(2π²∈₀R²) (-j)

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The specific brain mass: decreases if body mass increases.

Due to the specific brain mass is the ratio of brain mass to body mass is inversely proportional when the body mass increases, the specific brain mass decreases.

If we calculate the specific brain mass of a person with a brain mass of 2 kg and a body mass of 50 kg and then with a body mass of 60 kg we have:

specific brain mass (50 kg) = 2 kg/50 kg = 0.04

specific brain mass (60 kg) = 2 kg/60 kg = 0.03

We can state that the specific brain mass decreases if the body mass increases.

It is the amount of mass associated with a person's body

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Taking into account the definition of Scientific notation, the correct representation of 5,970,000 in scientific notation is 5.97×10⁶.

Scientific notation is a quick way to represent a number using powers of base 10.

The numbers are written as a product:

a×10ⁿ

where:

In this case, to write the number 5,970,000 in scientific notation, the following steps are performed:

Finally, the correct representation of 5,970,000 in scientific notation is 5.97×10⁶.

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According to the question, the truck will pass now with a frequency of 10.2×10⁻³Hz.

The number of waves that pass a fixed point in a unit of time is known as the frequency in physics. It is also the number of cycles or vibrations that a body in periodic motion experiences in a unit of time. When a body in periodic motion moves through a series of events or locations before returning to its initial state, it is said to have experienced one cycle or one vibration.

Explanation:

To find the frequency of the cyclist being passed by the truck,

f' = {(19.7+(-1.56))/19.7}×1/90

  = 10.2×10⁻³Hz.

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T=2ᴫ√(m/k) , T be the time period, m be the mass and k be the force per unit displacement.

To check the correctness of the above equation we are using DIMENSIONAL ANALYSIS THEOREM. After using the theorem we can say that the formula is dimensionally correct.

The dimension of a physical quantity is defined as the power to which the fundamental quantities are raised to express the physical quantity.  . Dimensions are physical quantities that can be measured. A dimension is a combination of length, breadth and height as [M], [L] and [T] respectively.

We shall use DIMENSIONAL ANALYSIS to check the correctness of the above equation. In this analysis , we shall try to check the dimensions on the LHS and RHS :

LHS:

{T}≡{time}

RHS:

{2π√(m/k)}≡{√(m/k)}

Or,{2π√(m/k)}≡{√(m/(force/x))}

Or,{2π√(m/k)}≡{√(M/(MLT⁻²/L))}

Or,{2π√(m/k)}≡{√(1/T⁻²)}

Or,{2π√(m/k)}≡{√T²}

Or,{2π√(m/k)}≡{T}≡{time}

So, LHS = RHS .

Hence, from the above prove we can conclude that, the equation is dimensionally correct.

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Check the correctness of formula, T=2ᴫ√m/k , T be the time period, m be the mass and k be the force per unit displacement.

Answer:

Answer is

[tex]4g \: m {s}^{ - 1} [/tex]

Explanation:

We have to find the initial velocity, u.

Final velocity is v = 0. And acceleration is due to gravity.

Now,

[tex]v = u + at[/tex]

[tex]0 = u + ( - g)m {s}^{ - 2} \times 4s[/tex]

[tex]u = 4g \: m {s}^{ - 1} [/tex]

Therefore, the final answer depends on the value of g.