The lob in tennis is an effective tactic when your opponent is nearthe net. It c
ID: 1665948 • Letter: T
Question
The lob in tennis is an effective tactic when your opponent is nearthe net. It consists of lofting the ball over his head, forcing himto move quickly away from the net (see the drawing). Suppose thatyou lob the ball with an initial speed of 17.0 m/s, at an angle of 46.5° above the horizontal. At this instant youropponent is 10.0 m away from the ball. He begins moving away fromyou 0.30 s later, hoping to reach the ball and hit it back at themoment that it is 2.10 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
First write the two equations for the proj motion, using . final position = initialpos + init velocity * time + (1/2) at2 . Horiz: D = 0 + 17.0*cos46.5 *t + 0 . Vertical: 2.10 = 0 + 17.0*sin46.5 * t -(1/2)*9.80*t2 . Use the vertical equation to find the time the ball is in theair: . 4.9 t2 - 12.3314t + 2.10 = 0 use the quadratic formula... . t = 2.3329 seconds . Then find the final horiz position: . D = 17.0 * cos46.5 * 2.3329 = 27.30 meters . So the person must run 27.30 - 10.0 = 17.30 meters . in a time of 2.3329 - 0.30 = 2.0329 seconds . for an avg speed of 17.30 /2.0329 = 8.51 m/s . Use the vertical equation to find the time the ball is in theair: . 4.9 t2 - 12.3314t + 2.10 = 0 use the quadratic formula... . t = 2.3329 seconds . Then find the final horiz position: . D = 17.0 * cos46.5 * 2.3329 = 27.30 meters . So the person must run 27.30 - 10.0 = 17.30 meters . in a time of 2.3329 - 0.30 = 2.0329 seconds . for an avg speed of 17.30 /2.0329 = 8.51 m/sRelated Questions
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