The lob in tennis is an effective tactic when your opponent is near the net. It
ID: 1955018 • 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 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 0.48 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
Begin by breaking down the components of the tennis ball that was hit.
v(x) = 15cos(50o)
v(y) = 15sin(50o)
To figure out when the ball reaches 2.10m above the launch point, we use the equation d = vot + .5at2
2.1 = 15sin(50o)t - 4.9t2
Solving for t, we get t = .19978s or 2.1453s. Since he starts moving .48s after the ball is hit, we can resonably disregard the former solution, as it reaches that height before he begins moving. Thus, t = 2.1453s.
Now, we use the x component to figure out how far the ball reaches in that time frame.
d = vt
d = 15cos50 * 2.1453 = 20.6842m
Since he starts 10m away from the ball initially, the distance he needs to travel is 20.6842 - 10 = 10.6842m
Now we need the amount of time that he has. He starts moving .48s after the ball is hit, meaning that he has 2.1453 - .48 = 1.666s to reach the ball.
We have distance and time, and d = vt
Rearranging, we get v = d/t
v = 10.6842m/1.666s = 6.42m/s
(all my numbers are rounded for simplicity, though my calculations involved exact numbers so the final answer is slightly different if you used the rounded numbers I presented)
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