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Problem 19 Medium Difficulty

A pursuit spacecraft from the planet Tatooine is attempting
to catch up with a Trade Federation cruiser. As measured by an
observer on Tatooine, the cruiser is traveling away from the
planet with a speed of 0.600$c .$ The pursuit ship is traveling at a
speed of 0.800$c$ relative to Tatooine, in the same direction as
the cruiser. What is the speed of the cruiser relative to the pur-
suit ship?

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Video Transcript

Okay, so in this problem, we have three objects we have. The planet between which we're going to represent is too small. Uh, since the planet is not moving, we can say that the planet is our, you know, sure reference frame. So we going to call reference frame s? We have been to space ships. That's represent is this box. This is a spaceship one. And this is the cruiser that we're trying to catch. Critical. Just be Okay. So what we have here, we know that the velocity off, eh relative to the planet of between is zero point nine. Let's see 0.9 0.8, actually, zero point eight c. You know, point eight c and we know that they speed off the cruiser relative to the between is just 0.6 c. No, let's remember about the concepts of relativity. We know that we always can see that the velocity off the first object that is moving relative to our inertial frame. It's V developed city off the second object that it's moving relative to the through the initial frame is you and it speed between the two in this speed between the two No inertial frames is V. And that's exactly what we have to calculate. What is the relative velocity between the cruiser and the pursuit ship? So we know that we have Ah, wait. Calculate. This is just the prime equals V minus you divided by one minus. You ve divided by C square where see is the speed of light. So we just need to put all the values in here and calculate this. So let's see, we have here that this is mm. 0.6, actually, 0.8 minus 0.6, divided by one minus little 0.8. That multiple eyes. You know, 0.6. I actually forget this season. Here we have a C. We have a seer. And here we have a C square is going to cross the FTC scratch. So the actual value here is just zero point tree 85. See? So we know that the pursuit ship is moving to War Cruiser because the velocity is positive. So relative will also to the A lot of TV speed is in this direction here, and that's defined or inserted to this problem. We just need to remember that V is the relative speed off the first move nor inertial reference ring relative to the reference rain, the initial frame and you is the second no inertial reference train relative to the inertial frame. So just remember this, and we always you always will be able to calculate this.

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