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, and 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 20.0 m/s at an angle of 53.0 degree to the horizontal. By how much does the ball clear or fall short of clearing the crossbar? Does the ball approach the crossbar while still rising or while falling? A firefighter, a distance d from a burning building, directs a stream of water from a fire hose at angle theta_i above the horizontal as in Figure P4.20. If the initial speed of the stream is v_i, at what height h does the water strike the building?

Explanation / Answer

19)    (a) Let it take t sec to reach the goal post, by:-
=>R = [Ux] x t
=>36 = ucos x t
=>36 = 20 x cos53* x t
=>t = 2.99 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 = 20 x sin53* x 2.99 - 1/2 x 9.8 x (2.99)^2
=>h = 3.95 m
Thus the ball will clear the crossbar with +(3.95-3.05 = 0.9 m)
(b) Let the ball take t sec to reach its maximum height
=>By t = usin/g
=>t = [20 x sin53*]/9.8
=>t = 1.63 sec
=>The ball falling, when it approaches the crossbar.

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