Question

With respect to the earth, object 1 is moving at speed 0.80 c to the right. Object 2 is moving in the same direction at speed 0.80 c with respect to object 1. How fast is object 2 moving with respect to the earth?

Answer 1

Answer:

0.976 c

Explanation:

$v_{1e}$ = velocity of object 1 relative to earth = 0.80 c

$v_{21}$ = velocity of object 2 relative to object 1 = 0.80 c

$v_{2e}$ = velocity of object 2 relative to earth

Velocity of object 2 relative to earth is given as

$v_{2e}= \frac{v_{1e} + v_{21}}{1 + \frac{v_{1e}v_{21}}{c^{2}}}$

$v_{2e}= \frac{0.80 c + 0.80 c}{1 + \frac{(0.80c)(0.80c)}{c^{2}}}$

$v_{2e}$ = 0.976 c