Question

Please help me! I don't want an answer, only, I need help figuring out how to tackle problems like these. Thank you in advance!

Athletes are running in a line of length l with the same speed v. Their trainer runs towards them with the speed u (u < v). Upon meeting the trainer, each athlete turns around and starts running with the same speed v in the opposite direction. What will be the length of the line once all athletes turn
around?

Answer 1

We can simplify the problem by changing the coordinate system from the earth to the trainers. In this coordinate system the trainer is approaching the athletes with a speed of u+v (do you see that?). The athletes appear to the coach to be running in place i.e. not moving. The length of the line l (or any line) is the same in both coordinate systems. The trainer reaches the lead runner at t= 0 and the last runner a time t=T (OK?) As the trainer passes each runner and they turn and follow the trainer with a new speed in the trainers coordinate system of v-u (got it?). So how far did the first runner travel by the time the trainer reached the last runner, the separation of the runners i.e., the length of the new line? ( You know, speed*time .) What speed and what time?