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 23.8 m/s at an angle of 52.0 degree to the horizontal. By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.) m Does the ball approach the crossbar (and cross above or beneath it) while still rising or while falling? rising falling

Explanation / Answer

velocity = 23.8 m/s at 52 degree

Horizontal velocity = 23.8 cos 52 = 14.65 m/s

vertical velocity = 23.8 sin52 = 18.75 m/s

Time to cover 36 m horizontal distance = 36/14.65 = 2.457 s

Vertical height at (t= 2.457) s = ut +0.5at2

= 18.75*2.457 -0.5*9.8*2.4572 = 16.49 m

a) So the ball clears the crossbar by 16.49 - 3.05 = 13.44 m

b) Time of flight = 2*18.75/9.8 = 3.83 s

Since the time to cross corssbar, t = 2.457 is more than half the total time of flight (>3.83/2) the ball has started falling.

Falling

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