Running returns tennis problem

https://isaacphysics.org/questions/running_return?board=3f100d12-b24a-42c3-af94-5dd640088a6a&stage=a_level
I’m struggling with part D. The answer to part A is 14, B is 6.7 and C is 13. I have tried assuming the accelerations are the same both ways. I calculated the time the tennis ball takes to travel diagonally across the court, which is 1.132374996 s. I then used suvat to calculate a distance x from B where he could reach back to B in 1.13 s with an acceleration 6.9 ms^-2. I think I might be messing up when the question states that some time later, after he has already moved from B, then the ball is hit from A back to B. But without knowing what that ‘some time later’ how can I calculate his distance?

Reply 1

lordaxil

Remember that the player is still moving towards C at the point when the ball is hit, so they start out with a non-zero velocity which has to be reversed by acceleration before they start to move towards B again. Part (c) gives a clue how to set this situation up, but the difference here is you don't know the time before ball was hit (hint: use a suvat formula that doesn't involve the time).