Two balls thrown to same height with opposite velocities at midpoint

[je55ica7]

A juggler throws two balls to the same height so that one is at the halfway point going up when the other is at the halfway point coming down. At that point:

Their accelerations are equal but their velocities are equal and opposite.

Right?

 

[Fermat]

Right.

Their accelerations are always g.

It doesn't matter what point you choose, whether half-way point, or no. The upward velocity will always be equal and opposite the downwards velocity.

 

[je55ica7]

but will the acceleration be -g at any point?

 

[Fermat]

It alll depends upon which direction you call the positive direction.

g always acts downwards.

If you choose downwards as the +ve direction, then g will be taken as +ve, +g. And the acceleration will be +g at all points.

If you choose upwards as the +ve direction, then g will be taken as -ve, -g. And this time the acceleration will be -g at all points.