A satellite moves east, taken as the positive x axis direction, at a speed of 0.5 c and a spaceship moves toward it (to the west) at a speed of 0.8 c as measured by an observer on the Earth. The speed of the satellite measured by an observer in the spaceship is
A) 8.7 c
B) 0.21 c
C) −0.21 c
D) 0.93 c
E) −0.93 c

Question

Quizplus · Accepted Answer

The correct answer is D.The speed of the satellite measured by an observer in the spaceship is given by the relativistic velocity-addition formula:$$v' = \frac{v - u}{1 - \frac{vu}{c^2}}$$where v is the speed of the satellite, u is the speed of the spaceship, and c is the speed of light.Plugging in the given values, we get:$$v' = \frac{0.5c - 0.8c}{1 - \frac{(0.5c)(0.8c)}{c^2}} = -0.93c$$Therefore, the speed of the satellite measured by an observer in the spaceship is -0.93c, which is choice D.

A Satellite Moves East, Taken as the Positive X Axis