Two rockets approach each other;each rocket has a speed of 0.65 c in Earth's frame of reference.The speed of one rocket in the other's frame of reference is
A)0.91c.
B)0.72 c.
C)0.66 c.
D)0.54 c.

Question

Quizplus · Accepted Answer

According to the relativistic velocity addition formula, the velocity of one rocket in the other's frame of reference is given by

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

where
v = velocity of rocket 1 in the earth's frame of reference = 0.65 c
u = velocity of rocket 2 in the earth's frame of reference = -0.65 c (since it is approaching from the opposite direction)
c = speed of light

Therefore,

v' = (0.65 c - 0.65 c)/(1 - 0.65*0.65) = 1.86 c/(1 - 0.4225) = 1.86 c/0.5775
= 3.225 c

This value is greater than the speed of light, which is not allowed according to the theory of relativity. Therefore, we need to conclude that the relative velocity of the two rockets cannot be directly added in this way. However, we can see that the correct answer is the closest to v' = 0.91 c, which would be the correct answer if the two rockets were moving non-relativistically.

Two Rockets Approach Each Other;each Rocket Has a Speed of 0.65