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Fluid Mechanics and Tennis Ball Motion

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A tennis player hitting from the baseline develops a forward velocity of 70 ft/s and a backspin of 5000 rpm. The ball weights 0.125 lb and has a diameter of 2.56 in. Assume standard pressure and 70 Fahrenheit and neglect the drag force. Including the lift provided by the backspin, how much will the tennis ball have dropped by the time it reaches the net 39 ft away?

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Solution Preview

Please see the attachment for the figure.

Let the produced by the back spin be H.
The horizontal velocity is 70 ft per sec which does not change with the lift as the lift is vertical.

The time taken by the ball to move from A to B covering a horizontal range of 39ft is ...

Solution Summary

This solution shows step-by-step calculations to determine how far the tennis ball would have dropped by the time it reaches the net that is 39 ft away, including the motion of backspin. An annotated diagram and brief explanations are provided.