A spaceship leaves Earth at a steady forward speed of 70% the speed of light.How fast relative to the ship must the spaceship launch a shuttlecraft in the forward direction so that it will be moving away from Earth at 98.7% the speed of light?
A)0.91c
B)0.97c
C)0.93c
D)0.99c
E)0.84c

Question

Quizplus · Accepted Answer

Let's use the relativistic velocity addition formula:

v = (u + v') / (1 + uv'/c^2)

Where:
u = velocity of the spaceship (0.70c)
v' = velocity of the shuttlecraft relative to the spaceship (what we're looking for)
v = velocity of the shuttlecraft relative to Earth (0.987c)
c = speed of light

Plugging in the values and solving for v', we get:

v' = (v - u) / (1 - uv/c^2) = (0.987c - 0.70c) / (1 - 0.987c * 0.70c / c^2) ≈ 0.93c

So the answer is (C) 0.93c.

A Spaceship Leaves Earth at a Steady Forward Speed of 70