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Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics by Robert B. Banks

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10

A Fast Way to Escape

Take a tennis ball and toss it straight upward. It goes to a certain height and falls back to your hands. Keep tossing or throwing the ball, each time with greater velocity. Observe that each time the ball goes higher and the total flight time is longer. An amazing observation! Anything else new? Most likely; we shall get to that shortly.

However, before going further we do magic: we remove all the air in the world. The resulting perfect vacuum greatly simplifies our mathematical analysis because now we can neglect the effect of air resistance. In this case, as we shall see, the height ym to which our tennis ball ascends is , where Uo is the velocity of the ball as it leaves your hand. The quantity g is the acceleration ...

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