Two particles are created in a high-energy accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650c, and the speed of each particle relative to the other is 0.950c. What is the speed of the second particle, as measured in the laboratory?

Video transcript

Hello, fellow physicist today, we're to solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use. In order to solve this problem, a tiny mass splits into two pieces with sufficient energy to move at speeds near the speed of light. The pieces take off in opposite directions. The speed of the particles relative to each other is 0.999 C. An observer at rest on earth determines one piece to be moving at 0.800 C find the speed of the other particle as determined by the observer. So that is our end goal is to find the speed of the other particle as determined by the observers. So we're looking at the observer's frame of reference. So we're given some multiple choice answers. They're all in terms of C where C represents the speed of light. So let's read them off to see what our final answer might be. A is 0.111 B is 0.999 C is 0.991 and D is 0.199. OK. So first off, let's name the two pieces A and B. So particle A and particle B, so let us state that piece A is attached to a moving frame and the particle and the frame move at and let's make a note of this move at U equals positive 0.800 C relative to a stationary frame used by the observer. And let us also state that piece B moves in the opposite direction towards the stationary frame, negative X prime direction of the moving frame. Its speed is 0.999 C relative to the moving frame. So VX prime is equal to plus positive 0.999 C. In the diagram here to the right helps us visualize our statements that we just made, it shows that B is moving towards are moving in the opposite direction towards the stationary frame. And it shows that piece A is attached to the moving frame. OK. So as we said before, our goal is to find the speed of the other particle as determined by the observer. So we need to find the value of VX. So V subscript X so we can find VX by recalling and using the equation for relativistic velocity transformation. So that equation states that VX is equal to VX prime plus U all divided by one plus U multiplied by VX prime all divided by C squared. So now we can plug in all of our known variables to solve for VX. So let's do that. So VX is equal to. So we know that VX prime is negative 0.999 C plus U which U is zero point 800 C divided by one plus U which U is 0.800 C multiplied by V prime which is negative 0.999 C all divided by C squared. So when we plug that into a calculator, we should get nag 0.991 C which is our final answer. So the negative sign means that VX points in the negative direction of the rest frame speed. Oh yeah, we jumped, we jumped up to the gun a little bit. So the negative sign means that VX points in the negative direction of the rest frame. So we can't say that negative 0.991 C is our final answer because speed also means the magnitude. So we need to take the absolute value of negative 0.991 C. So when we take the absolute value of a negative number, we get a positive number. So that means our final answer has to be positive 0.991 C and that is our final answer. So the speed is 0.991 C Fantastic. So that means the correct answer has to be the letter C 0.991 C. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.