With respect to the earth, object 1 is moving at speed 0.90 c to the right. Object 2 is moving to the left at speed 0.70 c with respect to object 1. How fast is object 2 moving with respect to the earth?
A)0.12 c
B)-0.20 c
C)0.54 c
D)0.20 c
E)1.6 c

Question

Quizplus · Accepted Answer

To find the speed of object 2 with respect to the earth, we use the relativistic velocity addition formula: $ v = \frac{v_1 + v_2}{1 + \frac{v_1 v_2}{c^2}} $. Here, $ v_1 = 0.90c $ and $ v_2 = -0.70c $. Plugging these values into the formula gives $ v = \frac{0.90c - 0.70c}{1 - \frac{0.90 \times 0.70}{1}} = 0.54c $.

With Respect to the Earth, Object 1 Is Moving at Speed