A 0.140-kg baseball is thrown with a velocity of 27.1 m/s. It is struck by the bat with an average force of 5000 N, which results in a velocity of 37.0 m/s in the opposite direction from the original velocity. How long were the bat and ball in contact?

Answers

Answer 1

Answer:

About \(1.795 \times 10^{-3}\) seconds

Explanation:

\(\Delta p=F \Delta t\), where delta p represents the change in momentum, F represents the average force, and t represents the change in time.

The change of velocity is:

\(37-(-27.1)=64.1m/s\)

Meanwhile, the mass stays the same, meaning that the change in momentum is:

\(64.1\cdot 0.14kg=8.974\)

Plugging this into the equation for impulse, you get:

\(8.974=5000\cdot \Delta t \\\\\\\Delta t= \dfrac{8.974}{5000}\approx 1.795 \times 10^{-3}s\)

Hope this helps!


Related Questions

A "laser cannon" of a spacecraft has a beam of cross-sectional area A. The maximum electric field in the beam is 2E. The beam is aimed at an asteroid that is initially moving in the direction of the spacecraft. What is the acceleration of the asteroid relative to the spacecraft if the laser beam strikes the asteroid perpendicularly to its surface, and the surface is not reflecting

Answers

Answer:

Acceleration of the asteroid relative to the spacecraft = 2ε\(E^{2}\)A/m

Explanation:

The maximum electric field in the beam = 2E

cross-sectional area of beam = A

The intensity of an electromagnetic wave with electric field is

I = cε\(E_{0} ^{2}\)/2

for \(E_{0}\) = 2E

I = 2cε\(E^{2}\)    ....equ 1

where

I is the intensity

c is the speed of light

ε is the permeability of free space

\(E_{0}\)  is electric field

Radiation pressure of an electromagnetic wave on an absorbing surface is given as

P = I/c

substituting for I from above equ 1. we have

P = 2cε\(E^{2}\)/c = 2ε\(E^{2}\)    ....equ 2

Also, pressure P = F/A

therefore,

F = PA    ....equ 3

where

F is the force

P is pressure

A is cross-sectional area

substitute equ 2 into equ 3, we have

F = 2ε\(E^{2}\)A

force on a body = mass x acceleration.

that is

F = ma

therefore,

a = F/m

acceleration of the asteroid will then be

a = 2ε\(E^{2}\)A/m

where m is the mass of the asteroid.


If an object is placed 15cm in of front of a concave mirror of radius Curvature 20cm. Determine the position of the image formed

Answers

The image will be formed at a distance of 30 cm in its front. Hence, this is the required solution.

Given that,

Object distance, u = -15 cm

The radius of curvature of the concave mirror, R = 20 cm

Focal length, f = R/2 = -10 cm (negative for concave mirror)

Let v is the distance between mirror and the formed image. Using mirror's formula to find it as :

\($\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$\)

\($\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$\)

\($\frac{1}{v}=\frac{1}{(-10)}-\frac{1}{(-15)}$\)

\($v=-30 \mathrm{~cm}$\)

So, the image will be formed at a distance of 30 cm in its front. Hence, this is the required solution.

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Two objects are dropped from a bridge, an interval of 1.0 s apart, and experience no appreciable air resistance. As time progresses, the DIFFERENCE in their speeds


a.
increases.



b.
remains constant.


c.
decreases.



d.
increases at first, but then stays constant.



e.
decreases at first, but then stays constant.

Answers

Answer: a

Explanation:

what is the processes found at a divergent boundary that helps form metamorphic rocks, igneous rocks, and sedimentary rocks. I need the process name for each one pls

Answers

At a divergent boundary, heat and pressure can cause metamorphism, magma can solidify to form igneous rocks, and sediments can accumulate and lithify to form sedimentary rocks. These three processes contribute to the formation of various types of rocks.

At a divergent boundary, three main processes occur that can lead to the formation of metamorphic, igneous, and sedimentary rocks:

1. Metamorphic rocks: Heat and pressure from the divergent boundary can cause existing rocks to be metamorphosed, or transformed, into new rocks with different textures and mineral compositions. This process is called metamorphism.

2. Igneous rocks: Magma, which is molten rock, can rise to the surface at a divergent boundary and cool and solidify to form igneous rocks. This process is called solidification or crystallization.

3. Sedimentary rocks: Sediments, such as sand and mud, can accumulate in the low-lying areas near a divergent boundary, such as in rift valleys or on the continental shelf. Over time, these sediments can be compacted and cemented together to form sedimentary rocks. This process is called lithification.

Hence, Heat and pressure at a divergent boundary can produce metamorphism, solidify magma to create igneous rocks, and accumulate and lithify sediment to create sedimentary rocks. Different sorts of rocks are formed as a result of these three processes.

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A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 100 cm wide at the top, and has height 60 cm. If the trough is being filled with water at the rate of 0.1 m3/min, how fast (in m/min) is the water level rising when the water is 10 cm deep

Answers

Answer:

0.238 m/min

Explanation:

The volume of water in the trough V =Ah' where A = area of cross-section = area of isosceles trapezoid = 1/2(a + b)h where a = length of bottom of isosceles trapezoid = 40 cm = 0.4 m, b =  length of top of isosceles trapezoid = 100 cm = 1 m and h = height of isosceles trapezoid = 60 cm = 0.6 m. So,

A = 1/2(a + b)h = 1/2(0.4 m + 1 m)0.6 m = (1.4 m)0.3 m = 0.42 m² and h' = height of water level in trough = H - h" where H = length of trough = 10 m and h" = depth of water level in trough = 10 cm = 0.1 m

So, V = Ah'

V = A(H - h") = A(10 - h")

Now, the rate of change of volume of the trough with respect to time dV/dt = d[A(10 - h")]/dt

dV/dt = -Adh"/dt

dh"/dt = -dV/dt/A

Since dV/dt = 0.1 m³/min, substituting the other variables into the equation, we have

dh"/dt = -dV/dt/A

dh"/dt = -0.1 m³/min/0.42 m²

dh"/dt = -0.238 m/min

This is the rate at which the depth is decreasing

Since the height h' = 10 - h"

dh'/dt = d(10 - h")/dt

= -dh"/dt

= -(-0.238 m/min)

= 0.238 m/min

So the water level is increasing at a rate of 0.238 m/min

How much impulse is imparted on a 0.14 kg baseball initially traveling at 32 m/s when it is struck by a baseball bat and begins to travel in the opposite direction at 49 m/s

Answers

ANSWER AND EXPLAINATION:
To calculate the impulse imparted on the baseball, we can use the impulse-momentum principle, which states that the impulse experienced by an object is equal to the change in momentum of the object. Mathematically, it can be expressed as:

Impulse = Change in momentum

The momentum of an object is given by the product of its mass and velocity:

Momentum = mass × velocity

In this case, the baseball has an initial mass of 0.14 kg and an initial velocity of 32 m/s. After being struck by the bat, it travels in the opposite direction at a velocity of 49 m/s.

Therefore, the change in momentum is given by:

Change in momentum = (mass × final velocity) - (mass × initial velocity)

Change in momentum = mass × (final velocity - initial velocity)

Change in momentum = 0.14 kg × (49 m/s - (-32 m/s))

Change in momentum = 0.14 kg × (49 m/s + 32 m/s)

Change in momentum = 0.14 kg × 81 m/s

Change in momentum = 11.34 kg·m/s

So, the impulse imparted on the baseball is 11.34 kg·m/s.

How many feet up high should I be required to wear a harness?

Answers

Answer:

About 6 feet or higher is recommended.  

Explanation

4.2 Determine the reactions of the loads L and R. ↓ 5m
↓ 7 kN 6m 3 kN 4m R (8)​

Answers

The reaction of load L is 0 (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).

How to find reaction?

To determine the reactions of the loads L and R, consider the equilibrium of the forces acting on the structure.

First, analyze the vertical equilibrium. The sum of the vertical forces must be zero:

ΣFy = R − 7 kN − 3 kN

ΣFy = 0

This gives:

R = 10kN

Next, analyze the horizontal equilibrium. The sum of the horizontal forces must be zero:

ΣFx = L

ΣFx = 0

This indicates that there is no horizontal force acting on the structure.

Therefore, the reaction of load L is zero (no horizontal force), and the reaction of load R is 10 kN (vertical upward force).

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24. A body A rests on a smooth horizontal table. Two bodies of mass 2 kg and 10 kg hanging freely, are attached to A by strings which pass over smooth pulleys at the edges of the table. The two strings are taut. When the system is released from rest, it accelerates at 2 m/s2 . Find the mass of A.

Answers

The two strings are taut. When the system is released from rest, it accelerates at 2 m/s2 then, Mass of A = 8m/5 kg.

Let the mass of the body A be ‘m’.

The two strings are taut so they exert a tension ‘T’ on body A.

Let ‘a’ be the acceleration produced in the system.

The free body diagram of body A is given below: mA + 2T = mA + ma = mA + m(2)mA + 10T = mA + ma = mA + m(2)

As the two strings are taut, we can say that tension in both strings is equal.

Therefore 2T = 10T or T = 5T As the body A is resting on a smooth horizontal table, there is no friction force acting on the body A.

The net force acting on body A is the force due to tension in the strings. ma = 2T – mg …(1)

As per the given problem, the system is released from rest.

Hence the initial velocity is zero.

Also, we are given that the system accelerates at 2 m/s2.

Therefore a = 2 m/s2 …(2)

From the equations (1) and (2), we get, m(2) = 2T – mg …(3)⇒ m(2) = 2×5m – mg⇒ 2m = 10m – g⇒ g = 8m/5

Thus, the mass of A is 8m/5 kg.

Answer: Mass of A = 8m/5 kg.

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What force in Newton is required to accelerate a car starting from rest to 20 m/s in 15 seconds if the mass of the car is 2500 kilograms?

Answers

Answer:

Explanation:

f =ma

F 2500 kg (20m/s-0m/s/15s)

F=2500kg(1.33m/s²)

F =3,325 N

f =ma, F 2500 kg (20m/s-0m/s/15s) and F=2500kg(1.33m/s²), F =3,325 N.

What is Force?

A push or pull that an object experiences as a result of interacting with another item is known as a force. Every time two items interact, a force is exerted on each of the objects.

The force is no longer felt by the two objects when the interaction ends. Only when there is interaction do forces actually exist.

Action-at-a-distance forces are those that happen even when the two interacting objects are not physically touching each other but are nevertheless able to push or pull against each other despite their physical separation. Gravitational forces are an example of action-at-a-distance forces.

Therefore, f =ma, F 2500 kg (20m/s-0m/s/15s) and F=2500kg(1.33m/s²), F =3,325 N.

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1. A material emits electrons when the electromagnetic radiation with a frequency equal to or less than the material's threshold frequency strikes the material.
True
False

2. In a particle model to show energy transfer, which of the following is correct?
a. Energy jumps are best described of electrons in packages known as photons
b. In energy transfers, electrons can absorb or emit energy
c. Photons carry energy from one location or object to another
d. All of the above are correct of particle models

Answers

1) The photoelectric effect is the phenomena by which, the metals release electrons when they are exposed to electromagnetic radiation with the suitable frequency. The photoelectrons are the electrons that are released in this process.

So, the statement is true.

2) In a particle model, energy transfer can be done through many ways such as:

The energy jumps between the particles in the form of photons.

Electrons can absorb or emit energy during energy transfer.

The energy is transferred between different objects in the form of photons.

So, all of them are true.

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A boy reaches out of a window and tosses a ball straight up with a speed of 10 m/s the ball is 20 m above the ground as he releases it use conservation of energy to find

Answers

The mass of the ball is approximately 10.24 kg, found using the conservation of energy principle.

What is the mass of a ball thrown upward with a speed of 10 m/s from a height of 20 m, using the conservation of energy principle?

To find the answer, we can use the conservation of energy principle, which states that the total energy of a system remains constant if there is no net work done on the system.

Initially, the ball has some potential energy due to its height above the ground and kinetic energy due to its motion. As it travels upwards, its potential energy increases while its kinetic energy decreases until it reaches its highest point, at which its kinetic energy is zero and its potential energy is at its maximum. Then, as it falls back down, its potential energy decreases while its kinetic energy increases until it reaches the ground, at which its potential energy is zero and its kinetic energy is at its maximum.

Let's use the following variables:

m = mass of the ball

v_i = initial velocity of the ball (10 m/s)

v_f = final velocity of the ball (0 m/s at the highest point)

h = height of the ball above the ground (20 m)

g =  (9.81 m/s^2)

The total energy of the ball initially is:

E_i = 1/2 * m * v_i^2 + m * g * h

At the highest point, the total energy of the ball is:

E_f = 1/2 * m * v_f^2 + m * g * 2h

Since the ball is at rest at the highest point, its final velocity is zero, so:

E_f = m * g * 2h

By the conservation of energy principle, the total energy of the ball is constant, so:

E_i = E_f

Substituting the expressions for E_i and E_f and solving for the mass of the ball:

1/2 * m * v_i^2 + m * g * h = m * g * 2h

1/2 * v_i^2 + g * h = 2g * h

m = (1/2 * v_i^2 + g * h) / g

m = (1/2 * 10^2 + 9.81 * 20) / 9.81

m = 10.24 kg

Therefore, the mass of the ball is approximately 10.24 kg.

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which of the following best describes why we have seasons on earth? view available hint(s)for part a which of the following best describes why we have seasons on earth? the tilt of earth's axis causes the northern hemisphere to be closer to the sun than the southern hemisphere in summer, and vice versa in winter. the tilt of earth's axis causes different portions of the earth to receive more or less direct sunlight at different times of year. earth's elliptical orbit means we are closer to the sun and therefore receive more intense sunlight at some times of year than at others. the varying speed of earth in its orbit around the sun gives us summer when we are moving fastest and winter when we are moving slowest.

Answers

Thee tilt of earth's axis causes the northern hemisphere to be closer to the sun than the southern hemisphere in summer, and vice versa in winter.

In this case, option A is correct.

Describe the seasons: Each season is a distinct time of year that can be recognized by special climatic characteristics. Every year, the seasons of spring, summer, fall, and winter follow one another. Each experiences cyclical patterns of light, climate, and weather every year.

Why are the seasons so important?

Soil saturation, precipitation patterns, river flows, lake concentrations, and snow cover are all impacted by seasonal variations in temperature and precipitation. Plants deteriorate and leaves fall as the wet and cold seasons approach. These alterations in the flora have an impact on the type and availability of food for humans and other animals.

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what is the velocity of the object 2.3 seconds after it is released from the top of the empire state building?

Answers

Explanation:

Object is under the effect of the acceleration of gravity

v = 1/2 a t^2       a = 9.81 m/s^2   t = 2.3

v = 25.9 m/s^2 = ~ 26 m/s   ( two significant digits)

A grandfather clock (with a pendulum) keeps perfect time on Earth. If you were to transport this clock to the Moon, would its period of oscillation increase, decrease, or stay the same? Would its frequency of oscillation increase, decrease, or stay the same? Explain.

Answers

Answer:

Frequency of oscillation will increase

Explanation:

Because The period of a pendulum is inversely proportional to the square root of the gravitational acceleration, so as. Gravity increases on the moon period of oscillation decreases whereas period of oscillating pendulum is inversely proportional to frequency thus frequency is directly proportional to gravity so as gravity increases on the moon the frequency will increase

Answer:

a) Therefore the period of oscillation in the moon will increase.

\(T_{E}<T_{M}\)

b) The frequency in the moon will decrease

\(\omega_{E}>\omega_{M}\)

Explanation:

The period of the pendulum is given by this equation:

\(T=2\pi\sqrt{\frac{L}{g}}\) (1)

As we can see, T is proportional to L and inversely proportional to the gravity vector. We know that g in the earth is grader than g in the moon.

\(g_{E}>g_{M}\) (2)

Therefore the period of oscillation in the moon will increase.

\(T_{E}<T_{M}\) (3)              

Now, the frequency of oscillation is:

\(\omega=\sqrt{\frac{g}{L}}\)

In this case, ω is proportional to g, then using (1) we can conclude that:

\(\omega_{E}>\omega_{M}\)

Therefore the frequency in the moon will decrease.

I hope it helps you!

           

Which TWO statements describe behaviors of particles that are related to the
physical properties of the materials?
A. They allow electrons to move freely between them.
B. They do not easily form bonds with atoms of other elements.
c. They change their positions relative to one another.
D. They combine with oxygen atoms to form a new substance.

Answers

Answer:

A and C I think

Explanation:

The two statements describe behaviors of particles that are related to the physical properties of the materials are A and C.

What is physical property?

Physical properties are measurable property whose value represents a condition of an object.

The two statements describe behaviors of particles that are related to the physical properties of the materials are ;

A. They allow electrons to move freely between them.

c. They change their positions relative to one another.

The two statements describe behaviors of particles that are related to the physical properties of the materials are A and C.

Hence, option A and C are correct.

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ill give brainliest if you say hi

Answers

Answer:

hi

Explanation:

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

I need help with the question 8B

I need help with the question 8B

Answers

The answer of this is C

a spring scale is constructed so that each 0.10-n increment is separated by 0.50 cm. what spring constant is necessary for the scale to be accurate?

Answers

Answer:

5.00

Explanation:

A tuna jumps out of the water with an initial velocity of 44 feet per second

Answers

Answer:

90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say i love you

Explanation:

plz do so it is true

6. A 15.53 kg bag of soil falls 5.50 m at a construction site. If all the energy is retained by the soil in the bag, how much will its temperature increase

Answers

The increase in the temperature of the soil when bag fall from the given height is 0.065 ⁰C.

The given parameters:

mass of the bag, m = 15.53 kgheight of fall, h = 5.5 mspecific heat capacity of soil, C = 0.200 kcal/kg ⁰C

Apply the principle of conservation of energy as follows;

\(mgh = mC \Delta T\\\\gh = C \Delta T\\\\\Delta T= \frac{gh}{C}\)

Convert the value of C in kcal/kg ⁰C  to  J/kg ⁰C

1 kcal = 4180 J

\(0.200 \ kcal/kg ^0 C= 0.2 \times 4180 (J/kg ^0C) = 836 \ J/kg^0 C\)

The increase in the temperature of the soil is calculated as follows;

\(\Delta T= \frac{gh}{C}\\\\\Delta T= \frac{9.8 \times 5.5}{836} \\\\\Delta T= 0.065 \ ^0C\)

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Use the image below to answer the following question (ruler not to scale).






If magnet B is moved closer to magnet A, how will magnetic potential energy be affected?
O. It will become zero.
O. It willincrease.
O. It will decrease.
O. It will stay the same.

Please help

Answers

Answer:

it depends on wether the + and - are facing eachother

or away from eachother

Explanation:

Answer:

Yes, they are correct, you need to include all parts of the question, don't just copy and paste the words. But in the diagram that was supposed to be there, the magnets' north poles are facing each other. Therefore they would push away from each other if they were to get any closer.  So, the magnetic potential energy would decrease due to their movement away from each other. So your answer is (C. It will decrease.

Explanation:

Suppose a 175kg motorcycle is heading toward a hill at a speed of 32 m/s. The two wheels weigh 12 kg each and are each annular rings with an inner radius of 0.280 m and an outer radius of 0.330 m.Randomized Variablesm = 175 kgv = 32 m/sh = 32 mA. How high can it coast up the hill. if you neglect friction in m?B. How much energy is lost to friction if the motorcycle only gains an altitude of 33 m before coming to rest?

Answers

A. The height the motorcycle can coast up the hill if friction is neglected is 1.63m.

B. Energy lost to friction before coming to rest is 56595J.

A. The height the motorcycle can coast up the hill, neglecting friction, is determined by the initial kinetic energy of the motorcycle. Using the equation for kinetic energy, KE = 1/2mv^2, we can calculate the initial kinetic energy of the motorcycle:

KE = 0.5 * 175kg * 32m/s^2 = 2800 J

The gravitational potential energy gained by the motorcycle is equal to the initial kinetic energy. Using the equation for gravitational potential energy, PE = mgh, we can calculate the height, h, the motorcycle can coast up the hill:

PE = 2800J = mgh

h = 2800J / (175kg * 9.8m/s^2) = 1.63m

Therefore, the motorcycle can coast up the hill to a height of 1.63m, neglecting friction.



B. The amount of energy lost to friction can be calculated using the equation for work, W = Fd. If the motorcycle only gains an altitude of 33m before coming to rest, then the force of friction, F, must be equal to the weight of the motorcycle, and the distance traveled by motorcycle, d, is 33m.

W = Fd = (175kg * 9.8m/s^2) * 33m = 56595J

Therefore, the amount of energy lost to friction is 56595J.

Therefore,

A. The height the motorcycle can coast up the hill if friction is neglected is 1.63m.

B. Energy lost to friction before coming to rest when altitude gained is 33m is 56595J.

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A wave has a wavelength of 1.5 meters and frequency of 125 Hz. What is the wave speed?

Answers

Just do 1.5 fidvide 125

A runner starting from rest reaches a velocity of 9.6 m/s in 2.0s. What is her average acceleration?

Answers

Answer:

Explanation:

From the given information if we assume that the runner didn't  come back to her original position.

Her initial velocity = 0 m/s

Final Velocity = 9.6 m/s

Time Taken = 2 seconds

She started from rest therefore her initial time would be 0 seconds.

We know that,

Average acceleration = (final velocity - initial velocity)/(final time - initial time)

=(v-u)/t1-t0

=(9.6 - 0)/(2-0) m/s^2

=4.8 m/s^2

An automobile has a mass of 1500 kg. What is the minimum uncertainty in the velocity (in miles per hour) when its center of mass is located with an uncertainty no greater than 1 cm

Answers

Answer:

\(\triangle v=1.57*10^-^3^5miles/hour\)

Explanation:

From the question we are told that

Mass of of automobile M= 1500 kg

Generally the equation of the uncertainty principle is  given by

\(\triangle p=\frac{h}{ \triangle x}\)

\(\triangle p=\frac{1.054*10^-^3^4}{ 10^-^2}\)

\(\triangle p=1.054*10^-^3^2\)

Generally the uncertainty in velocity is mathematically given by

\(\triangle v=\frac{\traingle p}{m}\)

\(\triangle v=\frac{1.054*10^-^3^2}{1500}\)

\(\triangle v=7*10^-^3^6m/s\)

Therefore the minimum uncertainty in the velocity (in miles per hour)

\(\triangle v=7*10^-^3^6*\frac{3600}{1609.3}\)

\(\triangle v=1.57*10^-^3^5miles/hour\)

In the same liquid, the pressures are equal at all points that are
A. the same distance below the liquid surface.
B. along the vertical walls of the container.
C. not touching any immersed objects.
D. not in the sunlight.

Answers

The correct option is A. which states that in the same liquid, the pressures are equal at all points that are at the same distance below the liquid surface.

This is because the pressure is determined by the weight of the liquid column above it, which is the same for all points at the same depth. The pressure along the vertical walls of the container is not equal because the liquid is in hydrostatic equilibrium which means that the pressure is not the same at all points in the liquid, and since the walls are vertical, the pressure is the same along them. The pressure at any point not touching any immersed objects is not equal to the pressure at any other point not touching any immersed objects because the pressure is determined by the weight of the liquid column above it, which is the same for all points not touching any immersed objects. The pressure is not affected by factors such as sunlight since the pressure at any point  in the sunlight is equal to the pressure at any other point not in the sunlight.

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The time-average power carried by a UPEMW propagating in vacuum is 0.05 W/m2. i) What is the amplitude value of the electric field and the amplitude value of the magnetic field in the wave

Answers

Answer:

The correct solution is "11.51 mA".

Explanation:

Given:

Time average power,

\(P_{avg}=0.05 \ W/m^2\)

n = 377

As we now,

⇒ \(P_{avg}=\frac{E_0^2}{n}\)

or,

⇒ \(E_0^2=0.05\times 377\)

⇒       \(=4.341 \ V\)

hence,

⇒ \(H_0=\frac{E_0}{n}\)

By putting the values, we get

         \(=\frac{4.341}{377}\)

         \(=11.51 \ mA\)

a certain compact disc (CD) contains 783.216 megabytes of digital information 4

Answers

Answer:

"a certain compact disc (CD) contains 783.216 megabytes of digital information 4"

A stuntman sitting on a tree limb wishes to drop vertically onto a horse galloping under the tree. The constant speed of the horse is 13.5 m/s, and the man is initially 3.55 m above the level of the saddle. Find a - What must be the horizontal distance between the saddle and limb when the man makes his move? Find b - How long is he in the air?

Answers

(a)  the horizontal distance between the saddle and limb when the man makes his move is approximately 11.386 meters.

(b)  the man is in the air for approximately 0.843 seconds.

To determine the horizontal distance between the saddle and limb when the man makes his move, we need to consider the horizontal velocity of the man when he drops from the tree limb.

Given:

Speed of the horse (constant velocity), v = 13.5 m/s

Vertical distance between the limb and saddle, h = 3.55 m

a) To find the horizontal distance, we can use the formula:

horizontal distance = horizontal velocity × time

Since the man drops vertically, his initial horizontal velocity is zero. The only horizontal velocity he will have is due to the motion of the horse.

The time taken by the man to fall can be determined using the equation for free fall:

h = (1/2) × g × t²

Where g is the acceleration due to gravity (approximately 9.8 m/s²) and t is the time.

Rearranging the equation, we get:

t = √(2h / g)

Substituting the given values:

t = √(2 × 3.55 / 9.8) ≈ 0.843 s

Now, we can find the horizontal distance:

horizontal distance = v × t

horizontal distance = 13.5 × 0.843 ≈ 11.386 m

Therefore, the horizontal distance between the saddle and limb when the man makes his move is approximately 11.386 meters.

b) The time the man is in the air can be calculated using the same equation for free fall:

t = √(2h / g)

Substituting the given value of h:

t = √(2 × 3.55 / 9.8) ≈ 0.843 s

Thus, the man is in the air for approximately 0.843 seconds.

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