An astronaut aboard a spacecraft enroute to Mars with a speed of 0.5c relative to Earth observes a meteor approaching head on at a speed of 0.9c.What is the speed of the meteor relative to Earth?
A)1.4c
B)-0.73c
C)0.4c
D)2.55c
E)None of these is correct.

Question

Quizplus · Accepted Answer

We can use the relativistic velocity addition formula to find the relative velocity of the meteor to Earth:

v = (v1 + v2) / (1 + v1*v2/c^2)

where v1 = 0.5c (velocity of the spacecraft relative to Earth) and v2 = -0.9c (velocity of the meteor relative to the spacecraft, with a negative sign indicating that it is approaching head-on). Plugging in the values, we get:

v = (0.5c - 0.9c) / (1 - 0.5c*(-0.9c)/c^2) = -0.73c

Therefore, the speed of the meteor relative to Earth is 0.73c, in the opposite direction to the spacecraft's motion.

An Astronaut Aboard a Spacecraft Enroute to Mars with a Speed