The lob in tennis is an effective tactic when your opponent isnear the net. It c
ID: 1736344 • Letter: T
Question
The lob in tennis is an effective tactic when your opponent isnear the net. It consists of lofting the ball over his head,forcing him to move quickly away from the net Suppose that you loftthe ball with an initial speed of v = 14.7 m/s, at anangle of q = 49.2° above thehorizontal. At this instant your opponent is d = 10.3 maway 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 ish = 2.02 m above its launch point. With what minimumaverage speed must he move? (Ignore the fact that he can stretch,so that his racket can reach the ball before he does.) The lob in tennis is an effective tactic when your opponent isnear the net. It consists of lofting the ball over his head,forcing him to move quickly away from the net Suppose that you loftthe ball with an initial speed of v = 14.7 m/s, at anangle of q = 49.2° above thehorizontal. At this instant your opponent is d = 10.3 maway 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 ish = 2.02 m above its launch point. With what minimumaverage speed must he move? (Ignore the fact that he can stretch,so that his racket can reach the ball before he does.)Explanation / Answer
vertical velocity of the ball=14.7*sin49.2=11.13 m/s vertical accleration=g=9.8 max. height reached by the ball=h v2=u2-2*g*h 0=11.132-2*9.8*h h=6.32 m time taken to reach max. height=t v=u-g*t 0=11.13-9.8*t t=1.14 s time taken by the ball to reach a height of 2.02 m from the launchpoint from the max. height=T s=u*T+(1/2)*g*T2 6.32-2.02=0+(1/2)*9.8*T2 T=0.88 s total time taken before the ball was 2.02 m above the launchingpoint=t+T=1.14+0.88=2.02 s horizontal velocity of the ball=14.7*cos49.2=9.61 m/s horizontal accleration=0 horizontal distance covered by the ball in 2.02s=9.61*2.02=19.412m in 2.02-0.4=1.62 s the he has to move (19.412-10.3)=9.112 m the minimum average speed should be 9.112/1.62=5.63 m/s
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