The lob in tennis is an effective tactic when your opponent is near the net. It

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. Suppose that you lob the ball with an initial speed of 15 m/s, at an angle of 50 degrees above the horizontal. At this instant your opponent is 10 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?

Explanation / Answer

The maximum height reached by the ball is H = (u2 * sin2/2g)----------(1) The range of the ball is R = (u2 * sin(2)/g) -----------(2) (1)/(2) (H/R) = [(u2 *sin2/2g)/(u2 * sin(2)/g)] = (1/4)* tan or (H/R) = (1/4) * tan or R = (4H/tan) here,H = 2.10 m and = 50o or R = (4 * 2.10/tan(50o)) = 7.0 m The distance of the ball from the opponent is S = 10 - 7.0 = 3.0 m we know that S = ut + (1/2)at2 u is the initial speed of the opponent,t is the time when theopponent starts moving away and a is the acceleration of theopponent. here,u = 0 and t = 0.30 s or 3.0 = 0 * 0.30 + (1/2)a * (0.30)2 or 3.0 = 0 + 0.045a or a = (3.0/0.045) = 66.7 m/s2 The minimum average speed with which he must move is v2 - u2 = 2aS or v2 - 02 = 2 * 66.7 * 3.0 or v2 = 2 * 66.7 * 3.0 or v = (2 * 66.7 * 3.0)1/2 = 20.0 m/s The minimum average speed with which he must move is v2 - u2 = 2aS or v2 - 02 = 2 * 66.7 * 3.0 or v2 = 2 * 66.7 * 3.0 or v = (2 * 66.7 * 3.0)1/2 = 20.0 m/s

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