Two boys on a merry go round

[Like Tony Stark]

Homework Statement

Two boys are sitting diametrically opposite on a merry go round. The platform has a constant angular velocity. Then, the boy $A$ throws a ball to the boy $B$. This ball has a horizontal velocity relative to the platform and directed to $B$, and has no horizontal acceleration. What's the acceleration with respect to $B$ along the plane of the platform at the instant after thrown?

Relevant Equations

$\vec a=\vec a_B + \vec{\dot \omega} \times \vec r + \vec \omega \times (\vec \omega \times \vec r) + 2. (\vec \omega \times \vec v_{rel}) + \vec a_{rel}$

This is a tipical Coriolis effect example, and I know what the trajectory drawn by the ball looks like from the perspective of B, and from the perspective of someone outside. But the acceleration with respect to $B$ is 0, isn't it? Because the problem says "the ball has no horizontal acceleration". If not, what would it be? I guess it would be an acceleration pointing outside the platform because that would be the acceleration that moves the ball from the perspective of $B$

 

[RPinPA]

Coriolis effect example, and I know what the trajectory drawn by the ball looks like from the perspective of $B$, and from the perspective of someone outside. But the acceleration with respect to $B$ is 0,

Do you see why the bolded phrases are contradictory? If $B$ perceives a path which is not straight in his frame of reference, then by definition the velocity can not be constant.

 

[Like Tony Stark]

Do you see why the bolded phrases are contradictory? If $B$ perceives a path which is not straight in his frame of reference, then by definition the velocity can not be constant.

I didn't express myself correctly. Yes, it has an acceleration because it doesn't follow a straight line, so it must have an acceleration. But how would that acceleration be? Because the task says "what's the acceleration of the ball with respect to $B$?#, which are its characteristics? It only has normal acceleration and not tangential because the velocity is constant, and it points outside the merry go round. Would that be ok?

 

[jbriggs444]

I didn't express myself correctly. Yes, it has an acceleration because it doesn't follow a straight line, so it must have an acceleration. But how would that acceleration be? Because the task says "what's the acceleration of the ball with respect to $B$?#, which are its characteristics? It only has normal acceleration and not tangential because the velocity is constant, and it points outside the merry go round. Would that be ok?

I am having difficulty following the logic here.

We have already agreed that the velocity is not constant. So it seems that you mean that the speed is constant because Coriolis is the only force in play. Indeed, Coriolis is always perpendicular to the velocity vector and does not affect speed. But that ignores the centrifugal pseudo-force. Centrifugal force can affect speed.