A spaceship travels at 0.746 c relative to Earth. If the spaceship fires a small

Question

A spaceship travels at 0.746c relative to Earth. If the spaceship fires a small rocket in the forward direction, how fast (relative to the ship) must it be fired for it to travel at 0.942c relative to Earth? (Choose the direction of the spaceship's motion relative to Earth as the positive direction.)
     c

Spaceship R is moving to the right at a speed of 0.352c with respect to Earth. A second spaceship, L, moves to the left at the same speed with respect to Earth. What is the speed of L with respect to R? (Enter your answer to four significant figures.) A spaceship travels at 0.746c relative to Earth. If the spaceship fires a small rocket in the forward direction, how fast (relative to the ship) must it be fired for it to travel at 0.942c relative to Earth? (Choose the direction of the spaceship's motion relative to Earth as the positive direction.)

Explanation / Answer

v2 = (v1 - v) / (1 - v/c^2 * v1)

v2 = .942 c      speed of rocket relative to earth

v = -.746 c    speed of earth relative to spaceship

v1 = .942 c (1 + .746 * .942) - .746 c

v1 = .8580 c

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