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, and half the crowd hopes the ball will clear the crossbar, which is 305 m high. When kicked, the ball leaves the ground with a speed of 23.0 m/s at an angle of 45.0 degree to the horizontal. By how much does the ball clear or fall short of clearing or fall short of clearing the crossbar? (Enter a negative answer if it falls short.) m Does the ball approach the crossbar while still rising or while falling rising falling

Explanation / Answer

the horizontal component of the velocity=23cos45=16.26m/sec time taken to reach 36m=36/16.26=2.214sec maximum height reached by the ball=(usin45)2/2g=(23sin45)2/19.6=13.49m
time taken by the ball to reach maximum height= usin45/g=23sin45/9.8=1.6595sec
so the ball cross the bar while falling. the height of the ball at time 2.214sec
y=23sin45-1/2*9.8*2.214*2.214= -7.758m
-ve sign indicates that the ball is falling but it is at a height of 7.758-3.05=4.708m so the ball will clear the bar by 4.708m

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