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.)

anonymous · Answer

Change in vertical position = 24.0 sin(46) t - (1/2) g t^2
Change in horizontal position = 24.0 cos(46)t

at max height,  24.0 sin(46)  - g t= 0 

this is roughly half-way through the motion.