The lob in tennis is an effective tactic when your opponent is near the net. It

Question

The lob in tennis is an effective tactic when your opponent is near the net. It consists of lofting the ball over his head, forcing him to move quickly away from the net (see the drawing). Suppose that you loft the ball with an initial speed of 15.0 m/s at an angle of 50.0° the horizontal. At this instant your opponent is 10.0 m away from the ball. He begins moving away from you 0.36 s later, hoping to reach the ball and hit it back at the moment that it is 2.10 m above its launch point. With what minimum average speed must he move? (Ignore the fact that he can stretch, so that his racket can reach the ball before he does.)

Explanation / Answer

First, find t when vertical distance is 2.1 m

H=(usin50)t-0.5gt2 = 2.1

t = 0.2 or t =2.14 (t=0.2 cannot be the answer here since the opponent starts moving at 0.36s later

t=2.14

Distance he has to run = (ucos50)t - 10 = 10.63m

Speed he need to move = 10.63/(2.14-0.36)= 5.97m/s

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