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 (see the drawing). Suppose that you loft the ball with an initial speed of 15.0 m/s at an angle of 50.0° the horizontal. At this instant your opponent is 10.0 m away 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 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.)

Please Show Work

Explanation / Answer

First calculate the time it takes the ball to reach 2.1m point above the ground

we have

h = votsin(50 deg) - 0.5gt^2

hence

2.1 = 15*t*sin(50 deg) - 0.5*9.81*t^2

2.1 = 11.49t - 4.9t^2

solution of this quadratic equation is

t1=0.20 (this time corresponds the moment then the ball is moving up)

t2=2.15 (this time corresponds the moment then the ball is moving down)

only the second solution is relevant as the delay of the player is 0.24 s

which is more than 0.2

during 2.15 sec the ball covered the horizontal distance of
d=vo*cos(50 deg)*2.15 = 20.73 meters, so the player needs to run back

20.73-10=10.73 meters and the time he has for that is

2.15-0.24 =1.91 seconds

so the average speed needs to be

V=d/t = 10.73/1.91 = 5.62 m/s

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