# Worksheet: Relativistic Velocity Transformation

In this worksheet, we will practice applying Lorentz transformation to determine the velocities of objects moving relative to each other at relativistic speeds.

Q1:

Suppose two spaceships A and B are moving toward each other. Spaceship A fires a missile at spaceship B. The speed of the missile, relative to spaceship A, is . The speed of the missile, relative to spaceship B, is . What is the relative velocity of the two spaceships?

• A
• B
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• D
• E

Q2:

Suppose a spaceship heading directly away from the Earth at can shoot a canister at relative to the ship.

What is the velocity of the canister relative to Earth if it is shot directly at Earth?

• A
• B
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• E

What is the velocity of the canister relative to Earth if it is shot directly away from Earth?

• A
• B
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• D
• E

Q3:

Suppose the speed of light were only 3,000 m/s. A jet fighter moving toward a target on the ground at 800 m/s shoots bullets, each having a muzzle velocity of 1,000 m/s. What are the bulletsβ velocity relative to the target?

Q4:

Two planets are on a collision course, heading directly toward each other at a speed of . A spaceship sent from one of the planets approaches the other planet at a speed of as measured in the reference frame of the other planet. What is the speed of the ship relative to its planet of origin?

• A
• B
• C
• D
• E

Q5:

A space probe speeding toward the nearest star moves away from Earth at . The probe sends radio waves toward Earth. The radio waves have a frequency of 1.00 GHz in the probeβs reference frame. What is the frequency of these radio waves as measured by a receiver on Earth?

Q6:

If a spaceship is approaching Earth at and a message capsule is sent toward it at relative to Earth, what is the speed of the capsule relative to the ship?

• A
• B
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• D
• E

Q7:

A moving object initially has a Lorentz factor which later becomes .

At what relative velocity is ?

• A
• B
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• D
• E

At what relative velocity is ?

• A
• B
• C
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• E

Q8:

Suppose a spaceship heading straight toward Earth at can shoot a canister at relative to the ship.

What is the velocity of the canister relative to Earth if it is shot directly at it?

• A
• B
• C
• D
• E

What is the velocity of the canister relative to Earth if it is shot directly away from it?

• A
• B
• C
• D
• E

Q9:

If two spaceships are heading directly toward each other at a relative velocity of , at what speed must a canister be shot from the first ship for the other ship to perceive the speed as ?

• A
• B
• C
• D
• E

Q10:

A muonβs proper lifetime is 2.2 Β΅s. An observer measures the muonβs lifetime as 7.05 Β΅s. What is the relative velocity of the muon to the observer?

Q11:

When a missile is shot from one spaceship toward another, it leaves the first at and approaches the other at . What is the relative velocity of the two ships?

• A
• B
• C
• D
• E