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The lob in tennis is an effective tactic when your opponent

Customer Question

The lob in tennis is an effective tactic when your opponent is near a net. Suppose you lob the ball with an initial speed of 15 m/s an an angle of 50 degrees above the horizontal. At that instant your opponent is 10 m away from the ball. He begins to move away at 0.3 s later, hoping to reach the ball and hit it back at the moment that it is 2.1 m above its launch point. With what minimum average speed must he move? (ignore the fact that he can stretch, so the tacket can reach the ball before he does)
Submitted: 5 years ago.
Category: Homework
Expert:  David replied 5 years ago.

David :

hello

David :

thanks for requesting my help

David :

here is the solution

David :

first calculate the time it takes the ball to reach 2.1 point above the ground
we have
h=vo*t*sin(50)-0.5gt^2
hence
2.1 = 11.49t - 4.9t^2
solution of this quadratic equation is
t1=0.20 (this time corresponds the moment then the ball is moving up)
t2=2.15 (this time corresponds the moment then the ball is moving down)
only the second solution is relevant as the delay of the player is 0.3
which is more than 0.2
during 2.15 sec the ball covered the horizontal distance of
d=vo*cos(50)*2.15 = 20.73 meters, so the player needs to run back
20.73-10=10.73 meters and the time he has for that is 2.15-0.3=1.85 seconds
so the average speed needs to be V=d/t = 10.73/1.85 =5.8 m/s

David :