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 24.0 m/s at an angle of 46.0° to the horizontal.
(a) By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.)

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 24.0 m/s at an angle of 46.0° to the horizontal.
(a) By how much does the ball clear or fall short (vertically) of clearing the crossbar? (Enter a negative answer if it falls short.)

dumbcow · Answer

$$x(t) = 24\cos(46) t$$
$$y(t) = -4.9t^2 +24\sin(46)t$$
setting y=0 will tell you how long football is in air
t = 3.52

plug thatinto x(t) to find how far the football goes
x = 58.68
so it goes way past the required 36m

now see if it clears the goalpost 
find time when x = 36, plug that into y(t)
t=2.15
y = 14.4

so it clears by about 11.35m