how much does the ball clear or not clear the crossbar

Question

a kicker needs to kick a football 36 meters away from the field goal.The ball must clear the 5.5 meter high crossbar. It is kicked traveling at a speed of 22 m/s at a 55° angle. 

Answer 1

Initial condition:

To calculate v_i-y use sin(θ) = opp/hyp or sin(55°) = y_i-y/22 meaning v_i-y = 22sin(55°) = 18.021 m/s

To calculate v_i-x use cos(θ) = adj/hyp or cos(55°) = y_i-x/22 meaning v_i-x = 22cos(55°) = 12.619 m/s

In the x-direction, the time it takes to go 36 meters at 12.619 m/s is 36/12.619 = 2.853 seconds

To find the height of the ball when x = 36 meters, use y = v_i-yt + (1/2)at² where vi-y = 18.021, t = 2.853 s, a = -9.81:

y = v_i-yt + (1/2)at²

y = (18.021)(2.853) + (1/2)(-9.81)(2.853²) = 11.5 m

Since the crossbar is at 5.5 m, the ball clears by 6.0 meters