Darryl throws a basketball at the gym floor. the ball bounces once on the floor and comes to rest in his coach’s hands. at which point are all the forces on the basketball balanced?

when the ball is at rest in his coach's hands.

Explanation:

The forces on the basketball are balanced when the basketball is not experiencing any acceleration. This happens when the ball is in his coach's hand: in fact, at that moment the ball is at rest, so it means that its acceleration is zero. According to Newton's second law, this also mean that the net force on the basketball is zero, so the forces on the ball are balanced:

where F is the net force, m is the mass of the ball and a is the acceleration.

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