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Physics36. Special RelativityConsequences of Relativity

Okay, one problem that we talked about in class today, in one of the clicker problems, was the following. You are sitting here on the earth and you observe one spaceship that is heading to the right at speed V, you observe another spaceship that's heading to the left also at speed V, and we let those V's be very big. Okay, we said that V is three quarters of the speed of light and the question was, what is the observed relative speeds between those two? Okay, and to do this properly, you need Einstein's velocity addition rule. And Einstein's velocity addition rule was the following: Vac equals Vab plus Vbc divided by one plus Vab Vbc, all over C squared. If these are both three quarter C, which is 0.75 C, What do we get for the relative speeds as observed by the people on the rocket ships? Well, we can take this 0.75 and plug it in for each of these Okay, the C squared cancels with that C because we're going to square it and we're going to end up with 1.5 on the top, and then on the bottom we have 1 plus 0.75 squared, and if you do 0.75 squared, what do you get? Well, that's the same as 9/16ths, which has to be a little bit bigger than a half, so I think this is probably around 1.5 C over 1.56 C, somebody confirm that in your calculator. Okay, and if you do this 1.5 over 1.56, that's pretty close to 1, there's no C on the bottom right? That's gone. That's pretty close to one but it's a little bit less, and I know the answer already because we did it this morning, it's 0.96 C. So, on one of your misconceptual questions in the beginning of your homework, it is question 26.13, it says this exact problem, right? Two spaceships heading toward each other at three-quarter C as measured by you on Earth, what do they measure in the spaceship, right? It's looking at this other one coming towards it, we know that anytime you make a measurement it can't be bigger than C, and so it has to be something less than C but it's pretty close to C in this case because of the way those velocities add up. Okay, any questions about -- about that stuff? You guys feeling all right?