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welcome to our third example video looking at the Lorentz transformations. And this video will consider a rocket that flies by a space station and shoots off a drone of some sort at some velocity relative to itself. Okay, so this is all relative to some space station. Okay, so we have our space station here that measures the rocket as moving at 0.9 the speed of light. So this is the speed of the rocket with with respect to the space station. Meanwhile, the rocket, when it fires off its fires off its drone here, it fires it off at a speed of 0.95 of the speed of light. So this is thieve a las it, er rather the speed of the drone with respect to the rocket. So we have the drone with respect to the rocket, and we have the rocket with respect to the space station. The question is, how fast is the drone moving? With respect to the space station? Well, we can say that speed is going to be equal to We have speed of with respect to a is equal to be plus V divided by one plus you be times we oversee squared. Okay, So the V here is the speed of the rocket. So that's going to be 0.9 c. Meanwhile, you be here is the velocity of the drone with respect to the rockets. So we have 0.95 C plus 0.9 c divided by one plus and we have you be again So that 0.95 c multiplied by 0.9 c, divided by C squared. So you see the seas down here in the denominator are going to cancel out, and we're going to end up with some percentage of the speed of light. Namely, will have you A is equal to 0.95 plus 0.9 divided by one plus 0.95 multiplied by zero point nine all times the speed of light. See, now, just looking at this, you will find that you are going to have a number or rather and multiplier here that is less than one. This ratio is less than one typing it into your calculator. You should find that it's about 0.997 the speed of light. So this is the speed of the drone with respect to the space station. Now, this is very much like the Galilean transformations we had before, where we did problems like this. It's just that we have to take into account. We have these new equations for making these transformations happen, so make sure you pay attention to how we're plugging things in and what all your different reference frames are.

University of North Carolina at Chapel Hill