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Two planets are on a collision course, heading directly towards each other at 0.250$c .$ A spaceship sent from one planet approaches the second at 0.750$c$ as seen by the second planet. What is the velocity of the ship relative to the first planet?

0.615$c$

Physics 103

Chapter 28

Special Relativity

Relativity

Cornell University

Rutgers, The State University of New Jersey

McMaster University

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well, relative velocity of the first planet with respect to the second planet is 0.2 five times the speed of light. So we is equal to zero point 250 times the speed of light. And this is the relative velocity of the first planet. Well, I do velocity velocity off the first planet off the first planet with respect to the second planet with respect to the second planet, Second planet and the relative lost two of the spaceship with respect to the second planet is you. And it's equal to zero point seven by zero times the speed of light. So this is the relative velocity off the spaceship off the past. You off this base ship with respect to the second planet with respect to the second to the second Planet planet? Well, no. Let's consider the relative velocity of the spaceship with respect to the first planet is you prime. So you prime is the relative velocity of this spaceship with respect to the first planet. Uh, you prime is Ah, relative velocity related velocity off the spaceship off the spaceship with respect to the first planet. With respect, uh, to the first first Planet Planet and using Einstein's like Mystic Lost Edition, you prime can be written, ese. Ah, you prime can be written is you minus V divided by one minus. You re divided by C square. Now let's substitute values You prime is equal to, um zero point 750 times the speed of light minus 0.250 times. Ah, the speed of light divided by divided by one minus uh, 0.75 Siegel see into 0.25 coc divided by do bi di bi C square. And this gives us 0.615 times the speed flight. So the velocity of the spaceship with respect to the first planet is 0.615 times this fetal.

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