As measured from the Earth,a spacecraft is moving at speed 0.80c toward another spacecraft moving at speed 0.60c in the same direction,i.e. ,the first spacecraft is catching up with the second spacecraft.What is the speed of the first spacecraft as viewed from the second spacecraft?
A)0.38c
B)-0.20c
C)-0.38c
D)not given

Question

Quizplus · Accepted Answer

To find the relative speed of the first spacecraft as viewed from the second spacecraft, we use the formula for the addition of velocities in special relativity: $v_{rel} = \frac{v_1 - v_2}{1 - \frac{v_1v_2}{c^2}}$, where $v_1 = 0.80c$, $v_2 = 0.60c$, and $c$ is the speed of light. Plugging in the values, we get $v_{rel} = \frac{0.80c - 0.60c}{1 - (0.80c \cdot 0.60c)/c^2} = \frac{0.20c}{1 - 0.48} = \frac{0.20c}{0.52} = 0.3846c$, which rounds to $0.38c$, making option A correct.

As Measured from the Earth,a Spacecraft Is Moving at Speed