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 0.35 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.)

Answer 1

The height of the ball is

y = x tanθ - g/2(v cosθ)^2 x^2

so, we have

y = 1.19x - .0527x^2

Now, we want x when y=2.10

1.19x - .0527x^2 = 2.10
x = 20.651

Now, since the ball's horizontal speed is 15 cosθ = 9.642 m/s, that means that it takes 2.14 seconds for the ball to reach the intended spot.

So, the opponent only has 1.79 seconds to move the required 10.651 meters, for a speed of 5.95 m/s

whew