The lob in tennis is an effective tactic when your opponent is near the net. It
ID: 1708544 • Letter: T
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 lob the ball with an initial speed of 19.0 m/s, at an angle of 55.0° above the horizontal. At this instant your opponent is 10.0 m away from the ball. He begins moving away from you 0.30 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
the ball with initial speed is v_0 = 19.0 m/s the ball hit it back at the moment that is y = 2.10 m The maximum flight time is t = - v_0 ± v_0^2 + 2ay / a t = - ( 19.0m/s sin 55 ) ± ( 19.0 m/s sin 55 )^2 + 2 ( -9.8 m/s^2 ) * ( 2.10 m ) / - 9.80 m/s^2 t = 3.03 s , 0.13 s As it travels upward the time of flight is t = 3.03 s horizontal distance travelled by the ball is x = v_0 cos * t = 19.0 m/s * cos ( 55 ) * 3.03 s = 33.0.2 m the opponent must move is 33.02 m - 10.00m d = 23.02 m minimum average speed is v_min = 23.02 m / ( 3.03 s - 0.30 s ) = 8.4 m/sRelated Questions
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