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 = 16.3 m/s, at an angle of θ = 51.4° above the horizontal. At this instant your opponent is d = 11.1 m away from the ball. He begins moving away from you 0.250 s later, hoping to reach the ball and hit it back at the moment that it is h = 2.00 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

Initial Horizontal and vertical components of velocities are

V_ox=16.3Cos51.4

V_oy =16.3Sin51.4

From Kinematic equation

Y=Y_o+V_oyt-(1/2)gt²

2=0+(16.3Sin51.4)t-(1/2)(9.81)t²

4.905t²-12.7388t+2=0

t=2.43 s

Horizontal distance

X=V_oxt =(16.3Cos51.4)(2.43)=24.7 m

Therefore opponent must move a distance

d=24.7-11.1 =13.6 m

and t =2.43-0.25 =

The minimum average speed must he move is

V_Avg =13.6/2.18 =6.24 m/s