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. Suppose that you loft the ball with an initial speed of v = 14.2 m/s, at an angle of = 48.8° above the horizontal. At this instant your opponent is d = 11.6 m away from the ball. He begins moving away from you 0.400 s later, hoping to reach the ball and hit it back at the moment that it is h = 2.17 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

Viy= 14.2 sin48.8=10.68 m/s

now y= viy t + 1/2 g t^2

2.17= 10.68 t -0.5 (9.8)t^2

-4.9t^2 +10.68t-2.17=0

we solve this quardatic equation for t,

t=1.953 s and t=0.227s

we choose the larger time and ball will be at height of 2.17 m at two times . we take larger time because at that time, the ball will be falling

so t= 1.953

now distance covered by ball in 1.953 seconds; d= vix t

x=14.2 cos 48.8 * (1.953)

x=18.27 m

so the opponent has to cover= 18.27-11.6=6.67m in 1.953-0.4=1.553 s

so average speed =v= 6.67/1.553

v=4.3m/s

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