A place-kicker must kick a football from a point 36.0 m (about 40 yards) from th

Question

A place-kicker 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 23.4 m/s at an angle of 51.0° to the horizontal (a) By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.) Tm (b) Does the ball approach the crossbar (and cross above or beneath it) while still rising or while falling? O rising falling

Explanation / Answer

(a) Let it take t sec to reach the goal post, by:-
=>R = [Ux] x t
=>36 = ucos x t
=>36 = 23.4 x cos51* x t
=>t = 2.44 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 = 23.4 x sin51* x 2.44 - 1/2 x 9.81 x (2.44)^2
=>h = 15.143 m
Thus the ball will clear the crossbar with +(15.143 -3.05 = 12.093 m)
(b) Let the ball take t sec to reach its maximum height
=>By t = usin/g
=>t = [23.4 x sin51*]/9.81
=>t = 1.85 sec
=>The ball falling, when it approaches the crossbar.

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