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Question

A spaceship leaves Earth traveling at $0.65 c$. A second spaceship leaves the first at a speed of $0.82 c$ with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired in the same direction the first spaceship is already moving.

Solution

VerifiedStep 1

1 of 2If the first ship is sent in the same direction as the first ship, people on Earth see them moving in the same direction, so the velocity of the second ship relative to the Earth is:

$\begin{align*} u&=\frac{v+u'}{1+\frac{vu'}{c^2}}\\ &=\frac{0.65c+0.82c}{1+\frac{(0.65c)(0.82c)}{c^2}}\\ &=\boxed{0.959c} \end{align*}$

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