A placekicker must kick a football from a point 360 m about

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 45.0° to the horizontal.

(a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer if it falls short.)

Solution

For a motion under the influence of gravitational acceleration, initial velocity u, launch angle as  , we have:

y = x tan – (gx² sec²)2u²

Here, x = 36 metres, = 45 and u = 23 m/s

That is, y = 36 - 9.81*36*36*2 / 2*23*23

y = 24.03 m

Therefore the ball will be at heigh of 24 metres while approaching the crossbar and hence will cross over it.