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 = 15.7 m/s, at an angle of = 51.5° above the horizontal. At this instant your opponent is d = 10.8 m away from the ball. He begins moving away from you 0.350 s later, hoping to reach the ball and hit it back at the moment that it is h = 2.17 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

What we want to solve for first is how long it will take the ball to reach a height of 2.17 m.

So we need to find the verticle velocity.
vy = v*sin 51.5 = 12.28m/s
y = vy*t -0.5gt^2
2.17 = (12.28)t - 0.5*9.8*t^2
We can use the quadratic formula to solve this
t = 2.31s, 0.191s

The later time is when the ball has started to come down again, so we should pick that. Now we need to know how far the ball has traveled horizontally during that time.
x = vx*t = vcos(51.5)*2.31 = 22.57 m

So our opponent needs to travel 11.77 m in 1.96seconds.

That's a velocity of11.77/1.96 = 6.00m/s

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