A 26.0 g ball is fired horizontally with initial speed v0 toward a 110 g ball that is hanging motionless from a 1.10 m -long string. The balls undergo a head-on, perfectly elastic collision, after which the 110 g ball swings out to a maximum angle θmax = 50.0. What was v0?


I think you need to find the tangential velocity using the angle that the ball swings to, but I am not sure how to go about beginning this problem.

The angle of the force is [tex]51.1^{\circ}[/tex]

Explanation:

To solve this problem, we can apply Newton's second law along the horizontal direction of motion of the suitcase:

[tex]\sum F_x = ma_x[/tex]

where

[tex]\sum F_x[/tex] is the net force along the x-axis

m is the mass of the suitcase

[tex]a_x[/tex] is the acceleration along the x-axis

The suitcase is moving at constant speed, so the acceleration is zero:

[tex]a_x=0[/tex]

Therefore the net force must also be zero:

[tex]\sum F_x = 0[/tex] (1)

We have two forces acting along the horizontal direction:

- The component of the push (forward) in the horizontal direction, [tex]F cos \theta[/tex], with

F = 43 N

[tex]\theta[/tex] = angle of the force with the horizontal

- The  force of friction, [tex]F_f = 27 N[/tex], backward

So the net force can be written as

[tex]\sum F_x = F cos \theta - F_f[/tex] (2)

Combining (1) and (2),

[tex]F cos \theta - F_f = 0[/tex]

And so we can find the angle:

[tex]\theta = cos^{-1}(\frac{F_f}{F})=cos^{-1}(\frac{27}{43})=51.1^{\circ}[/tex]

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1) Frequency: 1.95 Hz

2) Equilibrium position: 0.138 m

3) Amplitude: 0.357 m

4) Maximum speed: 4.36 m/s

5) Maximum acceleration: [tex]53.1 m/s^2[/tex]

6) Spring constant: 15.0 N/m

7) Total mechanical energy: 0.96 J

Explanation:

1)

The frequency of a simple harmonic motion is equal to the reciprocal of the period:

[tex]f=\frac{1}{T}[/tex]

where

f is the frequency

T is the period

For the particle in this problem, we have

T = 0.513 s (period)

So the frequency of motion is

[tex]f=\frac{1}{0.513}=1.95 Hz[/tex]

2)

In a simple harmonic motion, the object oscillates between two maximum positions [tex]+x_m[/tex] and [tex]-x_m[/tex] which are equidistance from the equilibrium position. So, the equilibrium position is the midpoint between these two positions.

For the particle in this problem, the two extreme positions are:

[tex]x_1 = -0.219 m[/tex]

[tex]x_2 = 0.495 m[/tex]

So the mid-point (the equilibrium position) is

[tex]x_{ep} = \frac{x_1 + x_2}{2}=\frac{-0.219+0.495}{2}=0.138 m[/tex]

3)

The amplitude of a simple harmonic motion is the maximum displacement of the object, measured from the equilibrium position.

This means that we can calculate the amplitude simply as the difference between one of the extreme positions and the equilibrium position.

Taking

[tex]x_2 = 0.495 m[/tex]

and

[tex]x_{ep} = 0.138 m[/tex]

We find the amplitude:

[tex]A=x_2 - x_{ep} = 0.495-0.138 =0.357 m[/tex]

4)

In a simple harmonic motion, the maximum speed is given by

[tex]v_{max}=\omega A[/tex]

where

[tex]\omega[/tex] is the angular frequency

A is the amplitude

The angular speed can be calculated from the frequency as follows:

[tex]\omega=2\pi f=2 \pi (1.95 Hz)=12.2 rad/s[/tex]

The amplitude is

A = 0.357 m

So, the maximum speed is

[tex]v_{max} = (12.2)(0.357)=4.36 m/s[/tex]

5)

The maximum acceleration in a simple harmonic motion is given by

[tex]a_{max}= \omega^2 A[/tex]

Where we already know that:

[tex]\omega=12.2 rad/s[/tex] is the angular frequency

A = 0.357 m is the amplitude of motion

Substituting, we find the maximum acceleration:

[tex]a_{max}=(12.2)^2(0.357)=53.1 m/s^2[/tex]

6)

The angular speed in a simple harmonic motion can be written as

[tex]\omega=\sqrt{\frac{k}{m}}[/tex]

where

k is the spring constant

m is the mass

Here we know that:

[tex]\omega=12.2 rad/s[/tex] is the angular speed

m = 0.101 kg is the mass of the particle

So we can solve the formula for k, the spring constant:

[tex]k=\omega^2 m =(12.2)^2(0.101)=15.0 N/m[/tex]

7)

Since the energy is conserved, the total mechanical mechanical energy is just equal to the maximum potential energy of the system, which occurs when the particle is at maximum displacement (x=A) and the speed is zero (so the kinetic energy is zero), therefore it is given by:

[tex]E=\frac{1}{2}kA^2[/tex]

where

k = 15.0 N/m is the spring constant

A = 0.357 m is the amplitude

And substituting,

[tex]E=\frac{1}{2}(15.0)(0.357)^2=0.96 J[/tex]

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Answer:

20ft/secs

Explanation:

60 feet/ 3 secs

Object 2 has more kinetic energy

Explanation:

The kinetic energy of an object is the energy possessed by the object due to its motion, and it is given by

[tex]K=\frac{1}{2}mv^2[/tex]

where

m is the mass of the object

v is its speed

In this problem, for object 1:

m = 2 kg

v = 2 m/s

So its kinetic energy is

[tex]K_1 = \frac{1}{2}(2)(2)^2=4 J[/tex]

For object 2,

m = 4 kg

v = 3 m/s

So its kinetic energy is

[tex]K_2 = \frac{1}{2}(4)(3)^2=18 J[/tex]

Therefore, object 2 has more kinetic energy.

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Answer:

Renewable energy sources 1.Cost more then nonrenewable resources and 2.Are so far not as reliable as nonrenewable energy.

Explanation:

renewable energy often has trouble creating the same amount of power that fossil fuels make because of its efficiency , they're expensive too

Answer:

[tex]v_0[/tex]=4.761 m/s

t=0.786 sec

Explanation:

In a projectile motion (or 2D motion), the object is launched with an initial angle [tex]\theta[/tex] and an initial velocity [tex]v_0[/tex]

The components of the velocity are

[tex]v_{ox}=v_ocos\theta[/tex]

[tex]v_{oy}=v_osin\theta[/tex]

Similarly the displacement has the components

[tex]x=v_{ox}.t=v_ocos\theta.t[/tex]

[tex]y=v_osin\theta.t-\frac{gt^2}{2}[/tex]

The last formula is valid only if the object is launched at ground level, as our frog does.  

There are two times where the value of y is zero, when t=0 (at launching time) and when it lands back from the air. We need to find that time t by making y=0

[tex]0=v_osin\theta.t-\frac{gt^2}{2}[/tex]

Dividing by t (assuming t different from zero)

[tex]0=v_osin\theta-\frac{gt}{2}[/tex]

Then we find the total flight as

[tex]t=\frac{2v_osin\theta}{g}[/tex]

Replacing this time in the formula of x

[tex]x=v_ocos\theta\frac{2v_osin\theta}{g}[/tex]

We can solve for [tex]v_o[/tex]

[tex]\displaystyle v_0=\sqrt{\frac{xg}{sin2\theta}}[/tex]

Knowing that x=2.20 m and [tex]\theta=54[/tex]°

[tex]\displaystyle v_0=\sqrt{\frac{xg}{sin2\theta}}=4.761m/s[/tex]

We now compute t

[tex]t=\frac{2v_osin\theta}{g}=0.786\ sec[/tex]

Final answer:

The launch speed of the frog is 4.81 m/s, and the time the frog spends in the air is 0.737 seconds.

Explanation:

A) Using the kinematic equation for projectile motion, we can find the launch speed. The launch speed, in this case, would be 4.81 m/s.

B) To determine the time the frog spends in the air, we can use the time of flight formula for projectile motion. The time in the air for the frog is 0.737 seconds.

The heat energy required is 2983 J

Explanation:

When an amount of energy Q is supplied to a certain sample of substance of mass m, the temperature of the substance increases by an amount of [tex]\Delta T[/tex] according to the equation :

[tex]Q=mC_s \Delta T[/tex]

where

Q is the heat supplied

m is the mass of the object

[tex]C_s[/tex] is the specific heat capacity of the substance

[tex]\Delta T[/tex] is the change in temperature

For the glass bottle in this problem:

[tex]m=53.0 g[/tex]

[tex]\Delta T = 92.0 - 25.0 =67.0^{\circ}C[/tex] is the change in temperature

[tex]C_s = 0.84 J/g^{\circ}C[/tex] is the specific heat of glass

Substituting into the equation, we find

[tex]Q=(53.0)(0.84)(67)=2983 J[/tex]

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Answer:

g'(10) = [tex]\frac{-1}{16}[/tex]

Explanation:

Since g is the inverse of f ,

We can write

g(f(x)) = x     (Identity)

Differentiating both sides of the equation we get,

g'(f(x)).f'(x) = 1

g'(10) = [tex]\frac{1}{f'(x)}[/tex]    --equation[1]    Where f(x) = 10

Now, we have to find x when f(x) = 10

Thus 10 = [tex]\frac{4}{x}[/tex] + 2

[tex]\frac{4}{x}[/tex] = 8

x = [tex]\frac{1}{2}[/tex]

Since f(x) = [tex]\frac{4}{x}[/tex] + 2

f'(x) = -[tex]\frac{4}{x^{2} }[/tex]

f'([tex]\frac{1}{2}[/tex])  =  -4 × 4 = -16            

Putting it in equation 1, we get:

We get g'(10) = -[tex]\frac{1}{16}[/tex]

Out of all given options, poor school performance  is a characteristic of sexually active teens.

Answer: Option B

Explanation:

Socio-demographic characteristics include age, gender and the highest level of education of the respondent. Most respondents had mothers with completed high school levels or diploma. Just over a quarter of respondents did not know their mother's highest education.  A low level of education and some family situations made the teen to be sexually active.

Teen sexual activity is "a fact in most African countries, as in most Western societies." There is a relationship between the sexual activity of young girls and their school resignation. Therefore, additional consequences of early sexual intercourse are women (and sometimes men) who drop out of school when they become pregnant.

Sexually active teens are more likely to come from single and step-parent families and have poor school performance.

The characteristic of sexually active teens is A and B are correct, which means they are more likely to come from single and step-parent families and have poor school performance.

While there may be studies suggesting correlations between certain factors, making broad statements about the behavior of sexually active teens based solely on family structure and school performance can be misleading.

Teenage sexual behavior is influenced by a variety of factors, including individual, family, cultural, and socioeconomic aspects. Family structure alone does not determine a teen's likelihood of engaging in sexual activity. Additionally, attributing poor school performance solely to family structure oversimplifies the complex interplay of factors influencing academic achievement.

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187500 Joules of work must be done to the 3000 kg car to change its speed from 10 m/s to 15 m/s.

Explanation:

Work is the measurement of the force on an object that overcomes a resisting force (such as friction or gravity) times the distance the object is moved. If there is no distance, there is no work, no matter what the effort.

Work done = Force * displacement

When you apply enough force on an object to overcome a resistive force, such that you move that object, you are doing work on that object. There is a relationship between that work and mechanical energy.

When an object is accelerated, you are doing work against inertia, such that the work equals the change in kinetic energy of the object.

Work done = Change in K.E

In the given case:

mass = m = 3000 kg

initial velocity = v₁ = 10 m/s

final velocity = v₂ = 10 m/s

Work = W = (1/2)m(v₂)² - (1/2)m(v₁)²

[tex]= \frac{1}{2}m(v2^{2} - v1^2)\\= \frac{3000}{2}(15^{2} - 10^{2})\\= 1500(225 - 100)\\= 1500*125\\= 187500 kg m^{2}s^{-2} \\= 187500 Nm\\= 187500 J[/tex]

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The net force on the car is zero

Explanation:

We can answer this question by applying Newton's second law of motion. In fact, we have:

[tex]\sum F = ma[/tex]

where

[tex]\sum F[/tex] is the net force acting on an object

m is the mass of the object

a is its acceleration

In this problem, the car is travelling with a constant velocity: this means that the acceleration of the car is zero (because acceleration is the rate of change of velocity). Therefore,

[tex]a=0[/tex]

So the equation becomes

[tex]\sum F = 0[/tex]

which means that the net force on the car is zero.

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Answer:

a. 12 m/s² down

Explanation:

Acceleration has units of length per time squared.  Acceleration is a vector, so it also has a direction.

Answer:

B. It must Be Heavy

Explanation:

An Object Can Have Mass And Be Light Such As A Pencil

The units for impulse are

[tex]N\cdot s[/tex]

Explanation:

We have two definition for impulse:

1) Impulse is defined as the product between the force exerted on an object and the time interval during which the force is applied:

[tex]I=F \Delta t[/tex]

where

F is the force, measured in Newtons (N)

[tex]\Delta t[/tex] is the time interval, measured in seconds (s)

From this definition it follows that Impulse can be measured in [tex]N\cdot s[/tex], which corresponds to option 3)

2)

Impulse is also defined as the change in momentum of an object:

[tex]I=\Delta p[/tex]

where

[tex]\Delta p[/tex] is the change in momentum of the object

The change in momentum has the same units of the change in momentum, so [tex]kg \cdot m \cdot s^{-1}[/tex], which corresponds to none of the options given

So the only correct option is

[tex]N\cdot s[/tex]

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The velocity of the wave is 40 m/s

Explanation:

The relationship between the velocity of a wave and its frequency and wavelength is given by

[tex]v=f \lambda[/tex]

where

v is the velocity

f is the frequency

[tex]\lambda[/tex] is the wavelength

For the ocean wave in this problem, we have:

[tex]\lambda = 10 m[/tex] (wavelength)

f = 4.0 Hz (frequency)

Therefore, its velocity is

[tex]v=(4.0)(10)=40 m/s[/tex]

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The velocity of an ocean wave with a wavelength of 10 m and a frequency of 4.0 Hz is 40 m/s.

The subject of this question is Physics, and more specifically, it deals with the topic of wave motion and wave velocity. The velocity of a wave can be calculated using the equation v = f × lambda, where v is the velocity of the wave, f is its frequency, and lambda is its wavelength.

Given that the wavelength lambda is 10 m and the frequency f is 4.0 Hz, we can substitute these values into the equation to find the wave velocity:

v = f × lambda = 4.0 Hz × 10 m = 40 m/s.

Therefore, the velocity of the ocean wave is 40 meters per second (m/s).

The correct choice is

A) I. Sound traveling faster through the air in the Sahara desert than in Antarctica.

Explanation:

Sound is a mechanical wave, which is a periodic disturbance of the space that propagates through vibrations of the particles in the medium filling the space. In particular, sound waves are longitudinal waves, in which the direction of oscillation of the particles in the medium is parallel to the direction of propagation of the wave.

Let's analyze now each statement:

I. Sound traveling faster through the air in the Sahara desert than in Antarctica.  --> TRUE. In fact, the higher the temperature of the air, the faster the sound propagates. In particular, there is a linear relationship between speed of sound and temperature of the air:

[tex]v=331.3 + 0.6T(^{\circ}C)[/tex]

where [tex]T(^{\circ}C)[/tex] is the temperature of the air in Celsius degrees.

II. An astronaut hearing the loud explosion of a ship from a mile away in space.  --> FALSE. This is not possible: in fact, sound is a mechanical wave, so it propagates only through a medium, and it cannot propagate in a vacuum (space is essentially vacuum, so sound cannot propagate in space).

III. Speeds and frequencies of sounds change as they pass through different mediums. --> FALSE. When a wave passes through different mediums, only the speed and the wavelength of the wave change, while the frequency remains the same.

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Answer:     I. Sound traveling faster through the air in the Sahara desert than in Antarctica.

Explanation:

Frequency stays the same as sound passes through different mediums. An explosion in space is not going to be heard if you are in the vacuum of space yourself.

Answer:

Velocity on the right side of the cart [tex]=0.09\ ms^{-1}[/tex]

Explanation:

Given

⇒The mass on the left of the cart [tex]m_1=1.5\ kg[/tex]

   Its velocity [tex]v_1=27\ cm/s[/tex],[tex]v_1=\frac{27}{100}=0.27\ m/s[/tex]

⇒Mass on the right of the cart [tex]m_2=4.5\ kg[/tex]

  Velocity[tex]=?[/tex] We have to find [tex]v_2[/tex]

From

The law of conservation of linear momentum:

We can say that.

Initial momentum will equalize the final momentum.

And momentum is the product of mass and its velocity.

Assigning one of its velocity as negative because both are in different direction.

Lets call [tex]v_1=-0.27m/s[/tex]

Recalling the formula and plugging the values.

[tex]m_1(-v_1)+m_2v_2=0[/tex]

[tex]v_2=-\frac{m_1(-v_1)}{m_2} =-\frac{1.5\times -0.27}{4.5} =0.09\ m/s[/tex]

So the velocity of the cart on the right side that has a mass of [tex]4.5\ kg[/tex] is [tex]0.09\ ms^{-1}[/tex]

Using the principle of conservation of momentum, the velocity of the right cart is calculated to be 0.09 m/s.

Given:

Step-by-Step Calculation:

Write the initial momentum equation:

Simplify the equation:

Solve for v2:

The negative sign indicates that the right cart moves in the opposite direction to the left cart. Hence, the velocity of the cart on the right is 0.09 m/s.

Answer: Infrared radiation

Explanation:

Infrared radiation is not visible to the human eye, since its wavelengths are outside the visible spectrum (between 700 nm and 1 mm), however this type of electromagnetic radiation is detected by the human body as heat.

These waves can be divided into:

- Near infrared or long wave infrared: it is the least sensitive to color and is easily absorbed by water.  

- Medium or medium wave infrared: it is also insensitive to color and easily absorbed by water and many types of plastics and paints.  

- Far infrared or short wave infrared: it is more penetrating than the long wave and is good for heating metals, these waves also can pass through clear materials.  This light has many uses, including heating lamps in physiotherapy and medical treatments, heat sensing devices, among others.

Answer:

a) The assumption that error theorists claim is at the heart of morality is that sincere moral judgments are always in error, therefore there is no moral knowledge possible.

Explanation:

Explanation:

Consider the kinematic equation,

[tex]x = vt + \frac{1}{2} a {t}^{2} [/tex]

where x is the distance traveled, v is the initial velocity, a is the acceleration and t is time. By plugging in known values and solving for x,

[tex]x = 3(1.8) + \frac{1}{2} (9.3) {1.8}^{2} [/tex]

through simple algebra we get

[tex]x = 20.466[/tex]

where this is the distance traveled in meters.

It means Constructive interference has occurred.

Explanation:

Waves travelling from opposite sides can collide to results into constructive interference or destructive interference.

In constructive interference, the crust of the waves merge.This results into increase in energy.In destructive interference the two waves cancel each other to cause loss of energy.

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Answer:

Constructive Interference

Explanation:

I'm Bill Nye the Science Guy

I also got 100% on my test

Answer:

900 grams

Explanation:

NB: 1litres=1000ml

Density=mass/volume

900kg/m³=mass/1000ml

mass =900kg/m³×100ml

mass=900grams

The mass of the alcohol in one liter of the mixture must be less than or equal to 0.9 kg, given that the density of the mixture is 0.9 kg/liter.

The key point to remember here is that the density of a solution is the ratio of its mass to its volume. Here, we are given that the density of the water-alcohol mixture is 900 kg/m3. Note that 1 m3 is equal to 1000 liters, so the density can also be expressed as 900 kg/1000 liters, or 0.9 kg/liter.

Since the question asks for the mass of the alcohol in one liter of the solution, and assuming that the entire liter is made up of the solution without any empty space, the mass of the solution in one liter would be 1 liter * 0.9 kg/liter = 0.9 kg.

Therefore, the mass of alcohol in one liter of the mixture must be less than or equal to 0.9 kg, assuming none of the mass is from any other substance. In order to find the exact mass of the alcohol, additional information would be required such as the ratio of water to alcohol in the mixture.

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Objects in motion tend to stay in straight-line motion at a constant speed, if no unbalanced forces are acting on them

(option: D. straight-line; constant)

Explanation:

This statement is exactly summarized by Newton's first law of motion, which states that:

"For an object moving by uniform motion (=at constant velocity or at rest), the object will maintain its uniform motion if no unbalanced  forces act on it".

This law essentially tells that if there is an object at rest, this will not move unless some external (unbalanced) force is applied on it, and if the object is moving by uniform motion (=constant speed in a straight line), it will continue moving with this motion unless some external (unbalanced) force is applied on it.

This law is generally difficult to prove in real-life situation, because there are always some unbalanced forces acting on objects. For instance, if we roll a ball along a table, if we neglect the friction between the table and the ball, the ball will continue moving with uniform motion forever. Of course this does not occur in real life, only because there is an external (unbalanced) force, the friction, that makes the ball slowing down and eventually stop.

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Answer:Answer: Normal force prevents the cup from falling to the ground. Explanation : When a cup is placed on a table, the forces acting on the cup are the gravitational force and the normal force. The gravitational force acts in the downward direction while the normal force acts in an upward direction

Explanation:

Answer:the answe would be joint comitee

Explanation:

The angle of incidence and the angle of reflection are measured from the B) normal to the surface.

Explanation:

Reflection is a phenomenon that occurs when a wave hits a boundary between two mediums and bounces back into the original medium.

The direction of the wave after reflection changes according to the law of reflection, which states that:

In this framework, the two angles are defined as follows:

Therefore, the complete sentence is

The angle of incidence and the angle of reflection are measured from the B) normal to the surface.

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Answer: The answer is B.

Explanation: i got it correct on Usatestprep.

Answer:

When reporting the speed, we need to include the value, units and direction the object was traveling.

It is a FALSE

Explanation:

Justification :

Answer:

Whats a potentiometer.

Explanation:

Some of the factors that can limit the accuracy of a potentiometer are internal temperature and Resistance change in the resistor

A potentiometer is a variable resistor that can be adjusted manually and has three terminals. A potentiometer is also called a pot

Potentiometers have different shapes and they are used in different in different application. A potentiometer can be used to control the volume of a radio. There are several types of a potentiometer.

some of the common ones include

However, some of the materials that can be used to construct potentiometers include

As stated earlier, the two factors that can limit the accuracy of a potentiometer are:

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a) The acceleration of gravity is [tex]4.96 m/s^2[/tex]

b) The critical velocity is 6668 m/s (24,006 km/h)

c) The period of the orbit is 8452 s

d) The satellite completes 10.2 orbits per day

e) The escape velocity of the satellite is 9430 m/s

f) The escape velocity of the rocket is 11,191 m/s

Explanation:

a)

The acceleration of gravity for an object near a planet is given by

[tex]g=\frac{GM}{(R+h)^2}[/tex]

where

G is the gravitational constant

M is the mass of the planet

R is the radius of the planet

h is the height above the surface

In this problem,

[tex]M=5.98\cdot 10^{24} kg[/tex] (mass of the Earth)

[tex]R=6.37\cdot 10^6 m[/tex] (Earth's radius)

[tex]h=2.60\cdot 10^6 m[/tex] (altitude of the satellite)

Substituting,

[tex]g=\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6 + 2.60\cdot 10^6)^2}=4.96 m/s^2[/tex]

b)

The critical velocity for a satellite orbiting around a planet is given by

[tex]v=\sqrt{\frac{GM}{R+h}}[/tex]

where we have again:

[tex]M=5.98\cdot 10^{24} kg[/tex] (mass of the Earth)

[tex]R=6.37\cdot 10^6 m[/tex] (Earth's radius)

[tex]h=2.60\cdot 10^6 m[/tex] (altitude of the satellite)

Substituting,

[tex]v=\sqrt{\frac{(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6 + 2.60\cdot 10^6)}}=6668 m/s[/tex]

Converting into km/h,

[tex]v=6668 m/s \cdot \frac{3600 s/h}{1000 m/km}=24,006 km/h[/tex]

c)

The period of the orbit is given by the circumference of the orbit divided by the velocity:

[tex]T=\frac{2\pi (R+h)}{v}[/tex]

where

[tex]R=6.37\cdot 10^6 m[/tex]

[tex]h=2.60\cdot 10^6 m[/tex]

v = 6668 m/s

Substituting,

[tex]T=\frac{2\pi (6.37\cdot 10^6 + 2.60\cdot 10^6)}{6668}=8452 s[/tex]

d)

One day consists of:

[tex]t = 24 \frac{hours}{day} \cdot 60 \frac{min}{hours} \cdot 60 \frac{s}{min}=86400 s[/tex]

While the period of the orbit is

T = 8452 s

So, the number of orbits completed by the satellite in one day is

[tex]n=\frac{t}{T}=\frac{86400}{8452}=10.2[/tex]

e)

The escape velocity for an object in the gravitational field of a planet is given by

[tex]v=\sqrt{\frac{2GM}{R+h}}[/tex]

where here we have:

[tex]M=5.98\cdot 10^{24} kg[/tex]

[tex]R=6.37\cdot 10^6 m[/tex]

[tex]h=2.60\cdot 10^6 m[/tex]

Substituting, we find

[tex]v=\sqrt{\frac{2(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6 + 2.60\cdot 10^6)}}=9430 m/s[/tex]

f)

We can apply again the formula to find the escape velocity for the rocket:

[tex]v=\sqrt{\frac{2GM}{R+h}}[/tex]

Where this time we have:

[tex]M=5.98\cdot 10^{24} kg[/tex]

[tex]R=6.37\cdot 10^6 m[/tex]

[tex]h=0[/tex], because the rocket is located at the Earth's surface, so its altitude is zero.

And substituting,

[tex]v=\sqrt{\frac{2(6.67\cdot 10^{-11})(5.98\cdot 10^{24}}{(6.37\cdot 10^6)}}=11,191 m/s[/tex]

Learn more about gravitational force:

brainly.com/question/1724648

brainly.com/question/12785992

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