The lob in tennis is an effective tactic when your opponent is nearthe net. It c

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 loft the ball with an initial speed of 15.0 m/s at an angle of50.0° the horizontal. At this instant your opponent is 10.0 maway from the ball. He begins moving away from you 0.24 s later,hoping to reach the ball and hit it back at the moment that it is2.10 m above its launch point. With what minimum average speed musthe move? (Ignore the fact that he can stretch, so that his racketcan reach the ball before he does.)
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 loft the ball with an initial speed of 15.0 m/s at an angle of50.0° the horizontal. At this instant your opponent is 10.0 maway from the ball. He begins moving away from you 0.24 s later,hoping to reach the ball and hit it back at the moment that it is2.10 m above its launch point. With what minimum average speed musthe move? (Ignore the fact that he can stretch, so that his racketcan reach the ball before he does.)

Explanation / Answer

initial vertical velocity=15*sin50 vertical acceleration=g=9.8 time taken to reach maximum height=t v=u-g*t 0=15*sin50-9.8*t t=1.17 s max height reached =h v2=u2-2*g*h 0=(15*sin50)2-2*9.8*h h=6.74 m time taken to fall 6.74-2.1=4.64 m from the max height=T u=0 s=u*T+(1/2)*g*T2 4.64=0+(1/2)*9.8*T2 T=0.97 s in 1.17+0.97 =2.14 s the ball traveled=15*cos50*2.14=20.63 mhorizontally in order to hit the ball 2.1 m from the ground he should move witha average velocity =(20.63-10)/2.14=4.97 m/s

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