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 lob the ball with an initial speed of 15.5 m/s, at an angle of 51.0° above the horizontal. At this instant your opponent is 10.0 m away from the ball. He begins moving away from you 0.30 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.)

Explanation / Answer

Firstly, using Newton's Laws of Motion in the vertical direction, we can find out the time in which the ball reaches 2.10 m above the lunch point.

h = u*t - 0.5*g*(t^2)

h=2.10 m

u=15.5 sin (51) m/s

g= 9.8 m/(s^2)

So, we get the quadratic:

4.9 t^2 - 12.05 t + 2.10 = 0

t = 2.27s , 0.19s

We need to take the larger of these times.

Hence, required t= 2.27s

Noe, finding the horizontal displacement of the ball in the maen time:

x= 15.5 cos(51) * t = 15.5 cos(51) * 2.27 = 22.14m

Distance that the opponent needs to travel = 22.14 - 10 = 12.14m

Time that the opponent has = 2.27 - 0.3 = 1.97s

Minimum average speed = 12.14/1.97 = 6.16 m/s

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