Don\'t understand this, please help. A placekicker must kick a football from a p

Question

Don't understand this, please help.

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 23.0 m/s at an angle of 52.0 degree to the horizontal. 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

Ball moves 36 m in horizontal with ux = 23cos52 = 14.16 m/s speed.

so time t = d / ux = 36/14.16 = 2.54 sec

In time ball's vertical height is y then,

y = uy*t + ay*t^2 / 2

y = (23sin52)*2.54 - 9.81*2.54^2 /2

y = 14.43 m

ball clear by = 14.43 - 3.05 = 11.34 m

b) total time of flight = 2usin@ /g = 2 * 23*sin52 / 9.81 = 3.70 sec

2.54 sec is time before max. heighht so it is still rising.

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