A block is supported on a compressed spring, which projects the block straight up in the air at velocity $\overrightarrow{\mathbf{v}}=v_{0y} \hat{\mathbf{j}}$ . The spring and ledge it sits on then retract. You can win a prize by hitting the block with a ball. When should you throw the ball and in what direction to be sure the ball hits the block? (Assume the ball can reach the block before the block reaches the ground and that the ball is thrown from a height equal to the release position of the block.)
A)At the instant when the block leaves the spring, directed at the block.
B)At the instant when the block leaves the spring, directed at the spring.
C)At the instant when the block is at the highest point, directed at the block.
D)At the instant when the block is at the highest point, directed at the spring.
E)When the block is back at the spring's original position, directed at that position.

Question

Quizplus · Accepted Answer

The ball and the block are both subject to gravity, moving in parabolic paths. The ball's path is dependent on the angle at which it is thrown, while the block's path is already determined by the compressed spring. As a result, the only way for the ball to hit the block is for their paths to intersect at some point. The highest point of the block's path is the point where its vertical velocity is 0, so the only chance for the paths to intersect is at this point. Therefore, the best choice is to throw the ball at the instant when the block is at its highest point, directed at the block itself.

A Block Is Supported on a Compressed Spring, Which Projects v→=v0yj^\overrightarrow{\mathbf{v}}=v_{0y} \hat{\mathbf{j}}v=v0y​j^​

A Block Is Supported on a Compressed Spring, Which Projects $\overrightarrow{\mathbf{v}}=v_{0y} \hat{\mathbf{j}}$