Which of the following statements is correct about the force of gravity between two objects

Based on the diagram, the correct statement is: Government and consumers make economic decisions in a mixed economy, while consumers make economic decisions in a market economy.

In a mixed economy, economic decisions are made by both the government and consumers.

The government plays a significant role in regulating and influencing economic activities through policies, regulations, and interventions.

In market economy, economic decisions are primarily made by consumers. The market forces of supply and demand dictate the allocation of resources, production levels, and pricing.

The freedom to buy and sell whatever they choose is what ultimately determines how commodities and services are produced and distributed.

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If the participants hadn't been reassigned, age would have been a confounding variable. Option D

A confounding variable is a variable that is associated with both the independent variable and the dependent variable.

In this case, age is associated with both video game playing and mood. Younger people are more likely to play video games, and they are also more likely to have better moods.

If the participants hadn't been reassigned, the difference in mood between the experimental and control groups could have been due to the difference in age, not the difference in video game playing.

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The rate energy is consumed this statement describes power.

Hence, Option C is correct answer.

Power is related to energy by that it is the rate at which energy is transferred.

It is a measure of the rate at which work is done.

According to the definition of power, Power is the amount of energy transferred or converted or consumed per unit time.

SI unit of power is watt.

By definition, 1 watt is equal to one joule of work done per second. So if P represents power in watts, E is the change in energy (number of joules) and t is the time taken in seconds then:

P=\(\frac{E}{t}\)= \(\frac{1 Joule}{1 Second}\)= 1 Watt.

Thus from the above conclusion we can say that, The rate energy is consumed describes power.

Hence, Option C is correct answer

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Answer:

μ = 0.849

Explanation:

In order to solve this problem we must remember that the friction force is defined as the product of the coefficient of friction by the normal force. And normal force is defined as the component of force in the opposite direction to the weight of the body (chair).

As in the y axis there is no movement we can say that the sum of the forces on the chair is equal to zero.

∑Fy = 0

\(N-W=0\)

where:

N = normal force [N] (units of Newtons)

W = weight of the chair = m*g [N]

m = mass = 15 [kg]

g = gravity acceleration = 9.81 [m/s²]

\(N=m*g\\N=15*9.81\\N=147.15 [N]\)

Now the key to solving this problem is to understand that we start applying force on the horizontal component until the chair starts to move at this moment the friction component is calculated with the static friction coefficient. As the chair doesn't move we can say that the sum of force in the horizontal direction is equal to zero.

∑Fx = 0

\(F -f_{force} = 0\)

F = force applied = 125 [N]

fforce = friction force = μ*N

μ = friction coefficient (static)

N = normal force = 147.15 [N]

\(125-u*147.15=0\\u = 125/147.15\\u = 0.849\)

Given:

Mass of cheetah (m) = 72.2 kg

Speed of cheetah (v) = 25.9 m/s

Equation:

\( \rm KE = \dfrac{1}{2} mv^2\)

Answer:

By substituting values in the equation, we get:

\( \rm KE = \dfrac{1}{2} \times 72.2 \times (25.9)^2 \\ \\ \rm = \dfrac{1}{2} \times 72.2 \times 670.81 \\ \\ \rm = 36.1 \times 670.81 \\ \\ \rm = 24,216.241 \\ \\ \rm \approx 24,200 \ J\)

\( \therefore \) Kinetic energy of cheetah = 24,200 J

The time it takes the marble to travel from P to M, obtained using the kinematic equation of motion is about 0.8 seconds

The kinematic equations of motion are four equations that describe the motion of an object undergoing constant acceleration.

The horizontal distance from P to N = 60 cm = 0.6 m

The vertical distance from N to M = 50 cm = 0.5 m

Let v represent the horizontal velocity of the mable, we get;

The duration it takes the mable to travel from P to N, t₁ = 0.6/v

The duration it takes the marble to reach the base of the table can be found using the kinematic equation of motion as follows;

h = u·t + (1/2)·g·t²

u = 0 (The initial vertical velocity is zero)

h = 0.5 meters

Therefore;

0.5 = (1/2) × 9.8 × t²

t² = 0.5/((1/2) × 9.8)

t = √(0.5/((1/2) × 9.8)) ≈ 0.32

The horizontal distance traveled during the time of flight of 0.4 meters indicates;

v = 0.4/0.32 ≈ 1.25

Therefore, t₁ = 0.6/v = 0.6/(0.4/0.32) ≈ 0.48

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The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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To determine the speed of B when A and B pass each other, we need to first gather information about their initial velocities, relative speeds, and direction of motion.

The speed of A is given and we need to find the speed of B. The formula for relative speed can be used, which states that the relative speed of two objects is equal to the sum of their individual speeds when they are moving in the same direction, and the difference of their speeds when they are moving in opposite directions. In this case, if A and B are moving in opposite directions, then their relative speed is equal to the speed of A plus the speed of B.

It is important to note that the speed of B must be expressed in the same unit as the speed of A (e.g. miles per hour) to allow for accurate comparison and calculation. Once the relative speed is known, it can be used to determine the speed of B by solving for it algebraically. The answer should be a numerical value in miles per hour.

It is also important to take into consideration any external factors that may affect the motion of the objects such as friction, air resistance, and changes in direction or speed. These factors can impact the accuracy of the calculation and should be accounted for if possible.

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Answer:Sound travel faster in warm room.

Explanation:The speed of sound depends on the temperature of the medium. Mathematically, the relation between the speed of the sound and the temperature is give by:v=

is the ratio of the specific heats

R is the gas constant

T is the temperature of the medium

We know that the temperature of the warm room is more as compared to the cold room.

So, it is clear that the sound travel faster in a warm room. The particles move faster when the temperature is high.            

The total distance covered during all three phases is approximately 882.375 m.

The car undergoes three phases: initial acceleration, constant speed, and deceleration.

In the first phase, it accelerates at 1.8667 m/s² for 15 seconds, covering 210.375 m.

In the second phase, it travels at a constant 28 m/s for 17 seconds, covering 476 m.

In the final phase, it decelerates at 2 m/s² for 14 seconds, covering 196 m.

The total distance covered during all three phases is approximately 882.375 m.

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The period of a pendulum is given by:

where L is the lenght of the pendulum and g is the acceleration of gravity.

We know that the repaired pendulum has a length of 114.63 cm, then its period is given by:

Therefore the repaired pendulum has a period of 2.149 seconds.

We know that a day has 86400 seconds, to determine how many swings the pendulum make in a day we divide the total amount of seconds in a day by the period of the clock, then we have:

Therefore the clocks swings 40200 times a day (rounded to three significant figrues)

The kinetic energy of the flywheel after 1 minute of rotation, given that it has a mass of 50 and radius of 40 cm is 32.4 KJ (Option D)

We'll begin by obtaining the velocity of the flywheel. This is shown below:

v = at

v = 0.6 × 60

v = 36 m/s

Finally, we shall determine the kinetic energy of the flywheel. Details below:

KE = ½mv²

KE = ½ × 50 × 36²

KE = 25 × 1296

KE = 32400 J

Divide by 1000 to express in KJ

KE = 32400 / 1000

KE = 32.4 KJ

Thus, the kinetic energy is 32.4 KJ (Option D)

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Answer:

potential energy is a form of energy that a body possess to its position.Potential energy is equal to potential energy is equal to mass times acceleration due to gravity times height.

The given scenario describes an experiment involving an electroscope, a glass bottle, a cardboard lid, a bolt or nail, a light wire, and an aluminum foil strip.

The purpose of the experiment is to demonstrate the behavior of electrons and their effect on the electroscope. Initially, when the electroscope is neutral, it means that there are equal numbers of protons and electrons on the foil leaves, causing them to hang down straight. The glass bottle and the cardboard lid act as insulators, preventing the rapid escape of electrons and maintaining equilibrium.

When the head of the bolt is touched with a plastic ruler that has been rubbed with fur or wool, the ruler gains excess electrons due to the process of friction. These excess electrons are transferred to the bolt since metal is a good conductor. The electrons then move down the bolt and accumulate on the foil leaves.

As the foil receives the additional electrons, the repulsive force between the like charges (electrons) causes the foil leaves to separate or fly apart from one another. This is a result of the electrostatic repulsion between the negatively charged leaves.

The purpose of using the glass bottle is to provide a protective barrier against air currents that could interfere with the experiment. It also allows observation of the behavior of the foil leaves as they move apart, indicating the presence of excess electrons.

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Answer:

a) Light that passes through the floor to reveal yourself (not shadow).

b) 2 rays of light that bounce between 2 transparent media.

c) I don't know what is Diffraction?

Answer:

Efficiency = 65%

Explanation:

The formula of Efficiency applied to any circumstance is:

Efficiency = Useful Energy / Energy applied

Then replacing the values given its:

Efficiency = 25 J / 32 J

Efficiency = 0.65

0.65 written as percentage is 65%, then:

Efficiency = 65%

As you do 32 joules of work using a pair of scissors and the scissors do 25 joules of work cutting a piece of fabric, the efficiency of the scissors is 78.125%.

Efficiency is the proportion of work done by a machine or throughout a process to the overall amount of energy or heat used.

The ratio of usable output to total input can be used to objectively measure efficiency. The efficiency of the device is defined as the ratio of energy converted to a useable form to the original amount of energy supplied.

Mathematically,

efficiency of a machine = (work output/work input)×100%

Given parameters:

Input work to the pair of scissors= 32 joules.

Output work from the pair of scissors= 25 joules.

Hence,

The efficiency of a machine = (work output/work input)×100%

= ( 25 joule/32joule)×100%

= 78.125%

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Answer:

1

Explanation:

The resultant is the sum of the two displacements having the same direction as the original vectors.

A displacement is described as a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.

Vectors in the same direction can be simply added to obtain the resultant vector.

We can describe vector as  a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

In conclusion, If we want to sum two vectors that are collinear and have the same sense, we can make that adding such as an algebraic sum.

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The resultant is the sum of the two displacements having the same direction as the original vectors. Option A

We know that there are generally two kinds of variables that we can be able to have in Physics, we have the scalars and the vectors. In the vectors we have the quantities that have both magnitude and direction while in the scalars we have the quantities that have only magnitude.

We know that when two vectors do have the same direction, we can be able to obtain the resultant vector by addition of the vectors together.

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Explanation:

Using Kinematics,

we have a = (v - u) / t.

Therefore a = (36m/s - 22m/s) / 5s = 2.8m/s².

Answer:

sinco

Explanation:

Answer:

the correct one is C

Explanation:

To find the answer, let's propose the solution of the problem

We create a system formed by the child and the platform so that all the forces have been internal and the angular momentum is conserved.

Initial instant. Before starting to walk

          L₀ = 0

Final moment. After the child is walking

          L_f = I₁ w₁ + m r v₂

where index 1 is used for the platform and index 2 for the child

linear and angular velocity are related

          v₂ = w₂ r

angular momentum is conserved

          0 = I₁ w₁ + m r (w₂ r)

          w₁ =  \(- \frac{m r^2}{I1} \ w_2\)

the moment of inertia of the platform bringing it closer to a disk or cylinder

         I₁ = \(\frac{1}{2}\) M r²  

sustitute

          w₁ = \(- \frac{2 m }{M} \ w_2\)

          W₁ = - \(- \frac{2 40}{30} \ w_2 = - \frac{8}{3} \ w_2\)

from here we can see that the platform and the child rotate in the opposite direction and with different angular speeds

when examining the answers the correct one is C

Answer:

Explanation:

relative to the ground the boy moves in a counter clockwise motion , now the boy and the wheel are one system

so by conservation of angular momentum their net sum of angular momentum relative to a point outside the system(say ground) should be zero

so the wheel moves in a clockwise direction , their angular velocity may or may not be same depending on I. so option D is wrong

option B is wrong because relative to ground their angular momentum should be equal and opposite

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The break shot speed of the player is determined as 96.5 ft/s.

use the following kinematic equation to determine the time of motion of the player.

h = vt + ¹/₂gt²

h = 0 + ¹/₂gt²

h = ¹/₂gt²

t = √(2h/g)

t = √(2 x 2.75/32.17)

t = 0.171 s

vx = x/t

vx = 16.5 ft / 0.171 s

vx = 96.5 ft/s

Thus, the break shot speed of the player is determined as 96.5 ft/s.

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Answer:

2.753*10^-11N

Explanation:

According to Newton's law of gravitation, the force between the masses is expressed as;

F = GMm/d²

M and m are the distances

d is the distance between the masses

Given

M = 3.71 x 10 kg

m = 1.88 x 10^4 kg

d = 1300m

G = 6.67 x 10-11 Nm²/kg

Substitute into the formula

F = 6.67 x 10-11* (3.71 x 10)*(1.88 x 10^4)/1300²

F = 46.52*10^(-6)/1.69 * 10^6

F = 27.53 * 10^{-6-6}

F = 27.53*10^{-12}

F = 2.753*10^-11

Hence the gravitational force between the asteroid is 2.753*10^-11N

The car is moving at approximately 12.5 meters per second.

The kinetic energy (KE) of an object can be calculated using the formula:

KE = 1/2 * m * \(v^2\)

where

KE = kinetic energy,

m =Mass of the object, and

v = velocity.

In this case, we are given the mass (m) of the car as 1600 kg and the kinetic energy (KE) as 125,000 J. To find the velocity .

Substituting the  values , we have:

125,000 J = 1/2 * 1600 kg *\(v^2\)

Now, we can solve for v by rearranging the equation:

\(v^2\) = (2 * 125,000 J) / 1600 kg

\(v^2\) = 156.25 \(m^2/s^2\)

Taking the square root, we find:

v = √156.25\(m^2/s^2\)

v ≈ 12.5 m/s

Therefore, the car is moving at approximately 12.5 meters per second.

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Answer:

48.4 m

Explanation:

To calculate the horizontal distance we need to find the flight time:

\( y_{f} = y_{0} + v_{0y}*t - \frac{1}{2}gt^{2} \)

Where:

\(y_{f}\) is the final height

\(y_{0}\) is the initial height

\(v_{0y}\) is the initial vertical speed

t is the time

g is the gravity

\( 0 = 36.0 m - \frac{1}{2}9.81t^{2} \)

\(t = \sqrt{\frac{2*36.0 m}{9.81 m/s^{2}}} = 2.71 s\)

Now, we can find the distance:

\( x_{f} = x_{0} + v_{0x}*t + \frac{1}{2}at^{2} \)

\(x_{f} = 12.0 m/s*2.71 s + \frac{1}{2}1.60 m/s^{3}(2.71 s)^{3} = 48.4 m\)

Therefore, the horizontal distance traveled by the rocket is 48.4 m.

I hope it helps you!

The resistance of the electric device using a power of 650 watts is approximately 27.7 ohms.

Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.

Hence

V = IR

R = V/I

Where V is the voltage or potential difference, potential difference, I is the current and R is the resistance.

We need to first find the electric current I.

Note:

Power = Voltage × Current.

Hence:

Current I = Power/Votage

Plug in the values

I = 650 / 120

I = 13/3 A

Substituting the values of voltage and current intio the above formula, we can calculate the resistance:

R = V/I

R = 120 / (13/3)

R = 27.7 ohms

Therefore, the resistance is approximately 27.7 ohms.

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Answer:

here ya go

Explanation:

When a force is applied to a car, the change in motion is proportional to the force divided by the mass of the car.

Answer:

Approximately \(-15.37m/s^2\)

Explanation:

The acceleration can be found using the formula:

\(x_{f} = x_{i} + v_{i} (t)+\frac{1}{2} (a)(t^{2} )\)

The work is as shown:

\(45m = 0 + 39 m/s (3.3s)+\frac{1}{2} a(3.3s)^2\)

\(45m=128.7m + 5.445s^2 a\)

\(-83.7m=5.445s^2a\)

\(a = -15.37190083m/s^2\)

a is about -15.37\(m/s^2\)

Answer:

Chapter 1

1. Show that the Lorentz transformation is such that the velocity of a light ray

travelling in the x direction is the same for the observer in the frame S and for

the observer in the frame S

.

Solution: Consider a light ray travelling in the x direction. If the light ray

connects two space–time points {t1, x1} and {t2, x2}, we have

c = x2 − x1

t2 − t1

The speed of light observed in the frame S will be

c = x

2 − x

1

t

2 − t

1

= c

γ ((x2 − x1) − βc(t2 − t1))

γ (c(t2 − t1) − β(x2 − x1))

= c

x2 − x1

t2 − t2

− βc

c − β x2 − x1

t2 − t2

= c

2. What is the mean path before decay for a charged pion with a kinetic energy of

1 GeV?

Solution: The pion has a lifetime 2.6 × 10–8 s and a mass of 139.6 MeV. If the

energy is 1 GeV, the velocity of the pion is 99% of the velocity of light (Eq. 1.4).

The mean path before decay is

= 0.99 c γ τ

= 0.99 c

1000 + 139.6

139.6

2.6 10−8 = 63 m

S. Tavernier, Experimental Techniques in Nuclear and Particle Physics, 271

DOI 10.1007/978-3-642-00829-0, C Springer-Verlag Berlin Heidelberg 2010

272 Solutions to Exercises

3. Show that the relativistic expression for the kinetic energy of a particle (Eq. 1.2)

reduces to the non-relativistic expression if the velocity of the particle is small

compared to the velocity of light.

Solution:

E = Ekinetic + m0c2 = m0c2

1 − (v/c)2

≈ m0c2

(1 − 1/2(v/c)2) ≈ m0c2(1 + 1/2(v/c)

2)

= m0c2 +

1

2

m0v2

4. For a Poisson distribution with average value 16, calculate the probability to

observe 12, 16 and 20 as measured value. Calculate the probability density function for a Gaussian distribution with average value 16 and dispersion 4, for the

values x = 12, 16 and 20. Compare the results.

Solution: For a Poisson distribution P(12) = 0.0829, P(16) = 0.1024, P(20) =

0.0418

For a Gaussian distribution, f(12) = 0.0605, f(16) = 0.0997, f(20) = 0.0605

5. Consider a very short-lived particle of mass M decaying into two long-lived particles 1 and 2. Assume you can measure accurately the energies and momenta of

the two long-lived particles. How will you calculate the mass of the short-lived

particle from the known energies and momenta of the two long-lived objects?

Solution: The mass of the short-lived particle, its energy and its momentum are

related by Eq. (1.1). The energy and momentum of the particle are equal to the

sums of the energy and sums of the momenta of the decay products, therefore

M2c4 = (E1 + E2)

2 − c2(P1 + P2)

2

6. Calculate the order of magnitude of the energy levels in atoms and in nuclei

using the ‘particle in a box’ approximation, Eq. (1.9). Use for the dimension of

the atom 10–10 m and for the dimension of the nucleus 10−15 m.

Solution: Atomic energy levels: ≈40 eV; nuclear energy levels: ≈400 MeV.

7 . Show that in a β− or a β+ decay only a very small fraction of the energy derived

from the mass difference goes to the kinetic energy of the final-state nucleon.

The electron is relativistic; therefore this requires a relativistic calculation! Hint:

the 3-body problem can be reduced to a 2-body problem by considering the

electron–neutrino system as one object with a mass of a few MeV.

Solution. Consider the 2-body decay of some heavy object with mass M into

two objects with masses m1 and m2. The kinetic energy of each of the final-state

particles in the overall centre of mass system is found as follows.

Solutions to Exercises 273

Consider two particles with energy and momentum four vectors p1 and p2.

The symbol pi stands for the four-vector {Ei,cpi}. The energy E appearing in this

expression is the total energy E, i.e. the rest energy mc2 plus the kinetic energy.

The four-vector product (p1.p2) is defined as

(p1.p2) =

(

E1E2 − c2 p1 p2

)

A four-vector product is a Lorentz invariant; this quantity can be evaluated in

any reference frame, and the result is the same. Consider now the quantity

(p1.p2)

m1c2

This is a Lorentz invariant. Evaluating this expression in the rest frame of

particle 1 makes clear that this is the energy of particle 2 seen in the rest frame

of particle 1. This remains true also if one of the particles is in fact a system

of particles, for example the system of the two particles 1 and 2. The energy of

particle 2, seen in the overall centre of mass frame of the particles 1 and 2 is

therefore

E∗

2 = (p1 + p2).p2

(p1 + p2)2

We have the following relations:

(p1 + p2)

2 = M2c4

(p1.p2) = 1

2

(

(p1 + p2)

2 − (p1)

2 − (p2)

2

)

= M2c4 − m2

1c4 − m2

2c4

And therefore finally

E∗

2 = M2c4 + m2

2c4 − m2

1c4

2Mc2

Let us now apply the above relation to the decay

N∗ → N + e− + ¯νe + Q

The symbol Q represents the energy liberated in the reaction. Let us denote

by M∗ the mass of the parent nucleus, by M the mass of the final-state nucleus

and by m the mass of the electron–neutrino system. The kinetic energy of the

nucleus in the final state is given by

274 Solutions to Exercises

Ekin = M∗2c4 + M2c4 − m2c4

2M∗c2 − Mc2

= M∗2c4 + M2c4 − m2c4 − 2M∗c2Mc2

2M∗c2

= (M∗ − M)

2 c4 − m2c4

2M∗c2

=

!

mc2 + Q

The energy of the cosmic ray photon is zero. his means that the photon had insufficient energy to create new particles, and instead, it simply scattered off the massive object.

Einstein's energy equation, also known as the mass-energy equivalence, relates the energy E of an object to its mass m and the speed of light c. The equation is:

E = mc^2

where:

E is the energy of the object in joules (J)

m is the mass of the object in kilograms (kg)

c is the speed of light in meters per second (m/s)

This equation means that mass and energy are interchangeable, and that a small amount of mass can be converted into a large amount of energy. The equation is an important consequence of Einstein's theory of special relativity, and it has been confirmed by numerous experiments, including nuclear reactions and particle accelerators.

Here in the Question,

We can use the conservation of momentum and energy to solve this problem. Since the two fragments have equal mass and are moving in opposite directions at the same speed, we know they have equal and opposite momenta. Therefore, the initial momentum of the photon must also be equal and opposite to the total momentum of the fragments.

Let's call the initial momentum of the photon p and the mass of each fragment m. The total momentum of the fragments is:

p' = 2mv

where v is the speed of each fragment, which we know is 0.6c. Therefore, we can write:

p' = 2m(0.6c) = 1.2mc

By conservation of momentum, we have:

p = -p'

where the negative sign indicates that the photon is moving in the opposite direction to the fragments. Therefore:

p = -1.2mc

Now we can use conservation of energy to relate the photon's energy E to its momentum p:

E^2 = p^2c^2 + m^2c^4

Substituting the expression we found for p, we get:

E^2 = (1.2mc)^2c^2 + m^2c^4

E^2 = 1.44m^2c^4 + m^2c^4

E^2 = 1.45m^2c^4

Solving for E, we get:

E = mc^2 * sqrt(1.45)

Plugging in the values for m and c, we get:

E = (0 * 9.0 × 10^16 kg) * sqrt(1.45) = 0

Therefore, The photon from a cosmic ray has no energy. This indicates that the photon was merely scattered off the large object since it lacked the energy to produce new particles.

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