The lob in tennis is an effective tactic when your opponent is near the net. It
ID: 2259047 • Letter: T
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 loft the ball with an initial speed of v = 18.5 m/s, at an angle of ? = 48.0
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 v = 18.5 m/s, at an angle of ? = 48.0 degree 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
Vxi = 18.5cos48=12.38
Vyi = 18.5sin48 = 13.75
h(t) = Vyi*t - 1/2 *9.8*t^2
2.10m = 4.9*t^2 -13.75*t
4.9*t^2 -13.75*t-2.10=0
Use quadratic formula
t = 2.9513s
Where is the ball horizontally at t = 2.081s *x
Vxi*t = 12.38*2.9513 = 36.53m from the launch point
The ball is 36.53-13.75= 22.78m from the opponent at the moment of launch
He has 2.9513-0.3 = 2.6513s to move 22.78m
= 22.78/2.6513s = 8.5920m/s or 8.60m/s(approx)
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