It's the question about Marry-go-round with physics, Help me!!?

Question

"Peter and Danny are standing on a merry-go-round which is turning counter-clockwise, as viewed from above. Peter throws a ball directly towards Danny. Does the ball get to Danny? If not, where does it go?"
I think the ball could not goes to Danny because thier linear velocities are different.The ball doesn't have centripetal force, so it won't rotate. But then, where would it go? would it go depends on the position where the two boys stand? it's really confusing and I don't have enough of physics conception. Please explain to me in detail. Thank you.

Answer 1

Let's not get involved with the Coriolis force. Let's just talk about it in the "lab frame".

Peter and Danny are opposite one another, and the mgr is going CCW. So let's consider the moment when Peter is at 9 o'clock and Danny is at 3 o'clock.

At that moment, Peter's velocity is down (i.e., if 12 o'clock is in the North, Peter's velocity would be Southwards); and Danny's velocity is exactly the opposite.

When Peter aims the ball at Danny, he will throw it in the direction 9 to 3 o'clock, or directly Eastwards. But Peter is already moving South, so from the lab point of view, the total velocity of the ball will be Eastwards plus Southwards. So the ball is already aimed a little south of Danny anyway, from our point of view.

To make matters worse, Danny himself is headed north. So the ball will miss him by twice as much.

Answer 2

The ball will go in the direction that's produced by a combination of Vinitial that's tangential to the merry-go-round and V that boy gives it with his hands. Add these 2 components vectorialy. This is where the ball will go relative to ground.