  Suppose that you loft the ball with an initial speed of v = 16.1 m/s, at an angle of θ = 51.8° above the horizontal. At this instant your opponent is d = 10.7 m away from the ball. He begins moving away from you 0.300 s later, hoping to reach the ball and hit it back at the moment that it is h = 2.02 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.)

Question

Suppose that you loft the ball with an initial speed of v = 16.1 m/s, at an angle of θ = 51.8° above the horizontal. At this instant your opponent is d = 10.7 m away from the ball. He begins moving away from you 0.300 s later, hoping to reach the ball and hit it back at the moment that it is h = 2.02 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.)

Step 1

Let t be the time, v be the initial velocity, g is the acceleration due to gravity. Using Newton’s equation of motion,

Step 2

Solving using quadratic formula,

Step 3

To find the average speed v...

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Kinematics 