At what point is the ball's vertical velocity at a minimum when thrown in the air?

The vertical velocity of the ball reaches its minimum at the peak of the trajectory. When a ball is thrown into the air, it initially has an upward velocity as it rises. As the ball ascends, it experiences a deceleration due to gravity, which continuously reduces its upward velocity. At the exact moment the ball reaches the peak, its vertical velocity becomes zero before it begins to descend.

This point is crucial because it marks the transition from upward motion to downward motion. After passing the peak, the vertical velocity becomes negative, indicating that the ball is falling back down. Thus, the peak of the trajectory is indeed where the ball's vertical velocity is at a minimum, as it changes from positive to negative.