Worksheet: The Lorentz Velocity Transformation

In this worksheet, we will practice calculating the velocity of an object in a reference frame that has a relative speed to the frame that the velocity was measured in.

Q1:

Consider two inertial reference frames, 𝑆 and 𝑆 . 𝑆 moves at a speed of 0 . 5 0 𝑐 relative to 𝑆 . An object moves at a speed of 0 . 2 0 𝑐 in 𝑆 . The motion of the object is antiparallel to the motion of frame 𝑆 relative to 𝑆 . What is the speed of the object in frame 𝑆 ? Give your answer as a multiple of 𝑐 to 2 significant figures.

  • A 0 . 2 7 𝑐
  • B 0 . 3 3 𝑐
  • C 0 . 6 4 𝑐
  • D 0 . 4 0 𝑐
  • E 0 . 2 0 𝑐

Q2:

A spaceship fires a projectile toward an enemy spaceship. The projectile moves at a speed of 0 . 1 0 𝑐 toward the enemy spaceship. Neither spaceship is moving relative to each other, but both are moving at a speed of 0 . 5 0 𝑐 relative to Earth. How fast does the projectile move toward the enemy ship in the reference frame of Earth? The motion of the projectile is parallel to the motion of the spaceships relative to Earth. Give your answer as a multiple of 𝑐 to 2 significant figures.

  • A 0 . 5 7 𝑐
  • B 0 . 6 3 𝑐
  • C 0 . 4 0 𝑐
  • D 0 . 4 5 𝑐
  • E 0 . 5 5 𝑐

Q3:

Consider two inertial reference frames, 𝑆 and 𝑆 . 𝑆 moves at a speed of 0 . 4 0 𝑐 relative to 𝑆 . An object moves at a speed of 0 . 1 0 𝑐 in 𝑆 . The motion of the object is parallel to the motion of frame 𝑆 relative to 𝑆 . What is the speed of the object in frame 𝑆 ? Give your answer as a multiple of 𝑐 to 2 significant figures.

  • A 0 . 5 0 𝑐
  • B 0 . 2 9 𝑐
  • C 0 . 4 8 𝑐
  • D 0 . 6 7 𝑐
  • E 0 . 3 1 𝑐

Q4:

A spaceship fires a projectile toward an enemy spaceship. The projectile moves at a speed of 1 . 4 × 1 0 m/s toward the enemy spaceship in the reference frame of Earth. Both spaceships are moving at a speed of 6 . 5 × 1 0 m/s relative to Earth. How fast does the projectile move toward the enemy ship in the reference frame of the spaceship it was fired from? The motion of the projectile is parallel to the motion of the spaceships relative to Earth. Give your answer to 2 significant figures.

  • A 6 . 2 × 1 0 m/s
  • B 2 . 2 × 1 0 m/s
  • C 8 . 3 × 1 0 m/s
  • D 1 . 8 × 1 0 m/s
  • E 6 . 8 × 1 0 m/s

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.