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Problem 24 Medium Difficulty

Two identical spaceships with proper lengths of 175 m are launched from Earth. Spaceship A is launched in one direction at 0.500$c$ and spaceship $B$ is launched in the opposite direction at 0.750$c .$ (a) What is the speed of spaceship $B$ relative to spaceship $A ?$ (b) What is the length of spaceship $A$ as measured by astronauts on spaceship $B?$


a) $0.4 \mathrm{c}$
b) $147 \mathrm{~m}$


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Video Transcript

Let's to part a ah, speed of space should be with respect to spaceship, eh? Yes. Let's say we and B is equal to speed off. Be with respect to art minus ah, speed off, eh? With respect to Earth divided by, uh, one minus we be times we and he divided by C Square. No, let's plug in the values we have. Ah, speed of special be with us Back to earth. It's equal to zero point 75 cedar times the speed of light minus 0.5 00 times the speed of light divided by divided by one minus. Um, 0.750 time See into 0.5. Is it Is it a time? See, divided by C square and solving for we, we is equal to the zero point toe. 50 times speed off light. Do I goodbye? A 0.62 five And excuse us. Is it a point for times the speed of light? Now let's do part B. Well, uh, lend of spaceship. A major from space will be, uh l equals crime into one minus B squared, divided by seas were one minus B squared, divided by C Square, found Let's plug in the values we have L Prime and Prime Musical to 1 75 meters on DDE one minus. The square will be zero point four time. See whole square, divided by C Square C square and simply finding is always equal to 1 75 into 0.84 and 1 75 times you point Kate, for it's equal to 1 47 meters.

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