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Problem 26 Easy Difficulty

A pulsar is a stellar object that emits light in short bursts. Suppose a pulsar with a speed of 0.950 $c$ approaches Earth, and a rocket with a speed of 0.995 $c$ heads toward the pulsar. (Both speeds are measured in Earth’s frame of reference.) If the pulsar emits 10.0 pulses per second in its own frame of reference, at what rate are the pulses emitted in the rocket’s frame of reference?

Answer

0.99987$c$

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Video Transcript

Well, speed off. Those are with respect with respect to rocket. Is we? We are This is the speed off bolts are with respect to rocket. And this speed is equal to, uh, speed off. Both are with respect to art minus speed off rocket with respect to art divided by one minus speed off. Both are with respect to earth multiply by speed off rocket that respect to earth divided by C square. Now let's substitute values we have ah, speed of both are with respect of earth is 0.95 times the speed of light minus and speed off. Rocket with respect to earth is minus zero point minus. Is it a point? A 995 times the speed of light divided by one minus. Well, uh, we have 0.9 five see into minus 0.9 mine five times the speed of light divided by C square. Well, solving this we get speed off. Balls are with respect to rocket. Uh is equal to 0.9 nine mine 87 times the speed of light

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