An earthbound radar monitors a spaceship moving at 0.9c. The crew of this first ship monitors a second ship following them at 0.8c with respect to them. What is the speed of the second ship as recorded by the earthbound radar?
A) 0.988c
B) 0.180c
C) 0.850c
D) 0.367c
E) 1.70c

Question

Quizplus · Accepted Answer

To find the speed of the second ship as recorded by the earthbound radar, we use the relativistic velocity addition formula: $ v = \frac{v_1 + v_2}{1 + \frac{v_1 v_2}{c^2}} $, where $ v_1 = 0.9c $ and $ v_2 = 0.8c $. Plugging in these values, we get $ v = \frac{0.9c + 0.8c}{1 + \frac{0.9 \times 0.8}{1}} = \frac{1.7c}{1.72} \approx 0.988c $.

An Earthbound Radar Monitors a Spaceship Moving at 0