A placekicker must kick a football from a point 36.0 m (about 40 yards) from the

Question

A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal. Half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 22.2 m/s at an angle of 47.0 degree to the horizontal. (a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer If it falls short.) It may be helpful to first determine the time required for the ball to reach the goal, m (b) Does the ball approach the crossbar while still rising or while falling?

Explanation / Answer

(a) Let it take t sec to reach the goal post, by:-
=>R = [Ux] x t
=>36 = ucos x t
=>36 = 22.2 x cos47* x t
=>t = 2.378 sec
Let the ball gain a height of h meter in t sec
=>By s = ut -1/2gt^2
=>h = [Uy]t - 1/2gt^2
=>h = usin x t - 1/2gt^2
=>h = 22.2 x sin47* x 2.378 - 1/2 x 9.81 x (2.378)^2
=>h = 10.874 m

the ball will clear the crossbar with 10.874-3.05 = 7.82 m

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