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Problem 22 Easy Difficulty

A spaceship travels at 0.750$c$ 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 0.950$c$ relative to Earth?

Answer

0.696$c$

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Video Transcript

rocket With respect to ship, we are s This is lost you off rocket with respect to ship is a cold too. Um lost t off rocket with respect to earth minus of lost your ship with respect to art divided by one minus we lost you off rocket with respect to earth a multiply by lost You have special with respect Oh, Earth divided by C square. Now let's plug in the values. Um, we have see the point mine Fine times The speed of light Still lost your rocket with respect to Earth Um minus but zero point seven five times the speed of light This is Ah, speed off the special with respect to earth divided by one minus See the point Mine five time See into 0.7 five times the speed of light Divided by si si And solving this We got, um zero point six 96 times the speed of light

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