The picture at the right shows a single frame from a video of a juggler tossing three balls up and down. In this frame, he has caught the central ball and is holding it so the ball is momentarily at rest. This corresponds to the time t = 0. In the video, he then throws the ball upwards, it goes upward, it reaches its highest point a few moments later, and then it comes most of the way down to his hand, but the video stops before he catches it again. Taking position and time data, the video analysis program finds velocity and acceleration for the ball at each time. A gif drawn from the full video can be watched by clicking on JugglerVideo.

A. Draw a system schema for considering the motion of the ball,

and free-body diagrams for ball at these instants:

• when he is holding it and accelerating it upwards,
• when he has released it and the ball is moving up,
• at the top when the velocity is 0, and
• when it is coming down before he catches it.

Label the forces in your free-body diagrams to indicate the type of force, who is causing the force, and who is feeling the force. Draw your diagrams so we can tell which forces are equal and which are larger. Use our standard notation for forces, F ^type_A→B.

B. Suppose the net force on the ball while it is in his hand can be approximated by the force vs. time graph shown at the right. Write an equation that would allow you to calculate the speed, v_I, with which the ball leaves his hand if you knew the values of F₀ (the maximum net force), m (the mass of the tennis ball), and t₀. Explain how you got this result.