A baseball player friend of yours wants to determine his pitching speed. You hav

Question

A baseball player friend of yours wants to determine his pitching speed. You have him stand on a ledge and throw the ball horizontally from an elevation 6.00 m above the ground. The ball lands 30.0 m away.

A) What is his pitching speed?

B) As you think about it, you’re not sure he threw the ball exactly horizontally. As you watch him throw, the pitches seem to vary from 5° below horizontal to 5° above horizontal. What is the range of speeds with which the ball might have left his hand? Enter the minimum and the maximum speed of the ball.

Explanation / Answer

a) time taken by ball to reach ground = (2*6/9.8)^0.5 = 1.11 s so, u*1.11 = 30 => u = 27.11 m/s b) if he throws at 5 above horizontal: ux = u.cos5 = 0.996u uy = u.sin5 = 0.087u so, -6 = 0.087u.t - 0.5*9.8.t^2 (taking upward direction as +ve) also, 0.996u.t = 30 on solving : u = 22.71 m/s if the ball is thrown 5 below horizontal: ux = u.cos5 = 0.996u uy = u.sin5 = -0.087u so, -6 = -0.087u.t - 0.5*9.8.t^2 also, 0.996u.t = 30 on solving : u = 36.27 m/s Answers: umin = 22.71 m/s umax = 36.27 m/s

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