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 6.0 m above the ground. The ball lands 25 m away.

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

1st case:-
=>let the ball take t sec to fall 6m
=>By s = ut + 1/2gt^2
=>6 = 0 + 1/2 x 9.8 x t^2
=>t = 1.22
=>t = 1.11 sec
=>By R = [Ux] x t
=>25 = u x 1.11
=>u = 22.52 m/s
2nd case(5° below horizontal):-
=>By R = [Ux] * t
=>25 = ucos5* * t
=>ut = 25.09 ----------(i)
=>By s = ut + 1/2gt^2
=>6 = usin5* t + 4.9t^^2
=>6 = 25.09 * 0.087 + 4.9t^2
=>t = 0.882 sec
=>By (i) :-
=>u = 25.09/0.882 = 28.44 m/s
3rd case(5° above horizontal) :-
=>=>By R = [Ux] x t
=>25 = ucos5* x t
=>ut = 25.09 ----------(i)
=>By s = ut + 1/2gt^2
=>6 = -usin5* x t + 4.9t^^2
=>6 = -25.09 x 0.087 + 4.9t^2
=>t = 1.29 sec
=>By (i) :-
=>u = 25.09/1.29 = 19.44 m/s

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