A man standing on the platform of a railroad station observes two trains approaching him from opposite directions at speeds of 0.5c and 0.75c,respectively.At what speed does one train move with respect to the other?
A)1.25c
B)0.25c
C)0.63c
D)0.91c
E)0.47c

Question

Quizplus · Accepted Answer

To find the relative speed of one train with respect to the other in the context of special relativity, we use the formula for addition of velocities: $v = \frac{v_1 + v_2}{1 + \frac{v_1 \cdot v_2}{c^2}}$, where $v_1 = 0.5c$, $v_2 = 0.75c$, and $c$ is the speed of light. Plugging these values into the formula gives $v = \frac{0.5c + 0.75c}{1 + \frac{0.5 \cdot 0.75}{1}} = \frac{1.25c}{1 + 0.375} = \frac{1.25c}{1.375} = 0.91c$.

A Man Standing on the Platform of a Railroad Station