*77.  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 15.0 m/s, at an angle of 50.0° 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.)

The ball will move a distance x, while the second player will move a distance x2.  The ball travels over a time t, while the player moves during a time t – 0.30 s.  So the average velocity of the player is

 

We find time by looking at the vertical displacement of the ball which is 2.10 m

 

 

We have a quadratic formula

Solving for t

 

Plug in values and find t

 

 

 

 

 

A time of 0.20 s is too short a time for the ball to travel across the net.  It is the time for the ball to go from ground to 2.10 m initially in a projectile motion.  SO the time needed is

2.14 s

 

Now use the horizontal motion to get the distance needed x

 

 

Again assuming no air resistance, plug in values

 

 

Now we can find the average speed

 

 

 

 

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This page last updated on January 11, 2020