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 (as shown in the figure below). Suppose that you loft the ball with an initial speed of v = 17.8 m/s, at an angle of = 49.4° above the horizontal. At this instant your opponent is d = 10.7 m away from the ball. He begins moving away from you 0.200 s later, hoping to reach the ball and hit it back at the moment that it is h = 2.03 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

given,

initial velocity 17.8 m/s

angle = 49.4 degree

distance of opponent = 10.7 m

height = 2.03 m

opponent begins moving after 0.2 sec

the ball will reach at height 2.03 m at time t so

by second equation of motion

2.03 = -17.8 * sin(49.4) * t + 0.5 * 9.8 * t^2

on solving we'll get t as 0.159 sec and 2.59875 sec

we will use the later one since at that time ball will be descending

distance travelled by the ball at 2.59875 sec

distance = 17.8 * cos(49.4) * 2.59875

distance = 30.1034 m

since opponent is already 10.7 m away from the thrower so total distance he has to cover = 30.1034 - 10.7

distance opponent has to cover = 19.4034 m

since opponent has started after 0.2 sec total time he got = 2.59875 - 0.2

since opponent has started after 0.2 sec total time he got = 2.39875 sec

speed = distance / time

speed of opponent = 19.4034 / 2.39875

speed of the opponent = 8.0889 m/s

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