Two spaceships are observed from earth to be approaching each other along a straight line. Ship A moves at 0.40c relative to the earth observer, while ship B moves at 0.60c relative to the same observer. What speed does the captain of ship A report for the speed of ship B?

Question

Quizplus · Accepted Answer

We use the relativistic velocity addition formula:

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

where u is the velocity of Ship A relative to the earth observer, v is the velocity of Ship B relative to the earth observer, and c is the speed of light.

Plugging in the values, we get:

v = (0.40c + 0.60c)/(1 + 0.40c*0.60c/c^2)
v = 1.00c/(1 + 0.24)
v = 0.81c

Therefore, the captain of Ship A will report that Ship B is moving at 0.81c relative to Ship A. The correct answer is C.

Two Spaceships Are Observed from Earth to Be Approaching Each