Question

Two rockets approach each other. Each is traveling at 0.75c in the earth’s reference frame. What is the speed, as a fraction of c, of one rocket relative to the other?

Short answer

speed of one rocket relative to the other is 0.96 c.

Step-by-step solution

Given information

We have given that, two rockets approaching each other. Each is traveling at 0.75c in the earth’s reference frame.

Step 1.

Let S be the earth’s frame of reference and S′ be rocket's frame of reference. S′ moves relative to S with v = -0.75 c. The speed of the second rocket in the frame S is u = 0.75c.

Step 2.

Using the Lorentz velocity transformation equation :

$u\text{'}=\frac{u-v}{1-{\displaystyle \raisebox{1ex}{$uv$}\!\left/ \!\raisebox{-1ex}{$c^2$}\right.}}$

$u\text{'}=\frac{0.75c-(-0.75c)}{1-{\displaystyle \raisebox{1ex}{$(0.75c)(-0.75)$}\!\left/ \!\raisebox{-1ex}{$c^2$}\right.}}$

$u\text{'}=0.96c$