Athletics: Juggling If you toss a ball h feet straight up, it will return to your hand after T(h) = 0.5√h seconds. This leads to the juggler’s dilemma: Juggling more balls means tossing them higher. However, the square root in the above formula means that tossing them twice as high does not gain twice as much time, but only √2 ≈ 1.4 times as much time. Because of this, there is a limit to the number of balls that a person can juggle, which seems to be about ten. Use this formula to find:
a. How long will a ball spend in the air if it is tossed to a height of 4 feet? 8 feet?
b. How high must it be tossed to spend 2 seconds in the air? 3 seconds in the air?
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