Question

20. A place kicker must kick a football from a point 35 m (about 38 yd) from the goal, and the ball must clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 23 m/s at an angle of 51◦ to the horizontal. To determine if the ball approaches the crossbar while still rising or while falling, what is its vertical velocity at the crossbar? Answer in units of m/s.

Answer 1

Initial vertical V of kick = (sin 51 x 23)

= 17.87m/sec.
Horizontal component = (cos 51 x 23)

= 14.47m/sec.
Time to crossbar = (35/14.47)

= 2.418 secs.
Time to max. height = (v/g) = (17.87/9.8)

= 1.823 secs.
Max. height = (v²/2g)

= (17.87²/19.6) = 16.29 metres.
Time ball falls from max height = (2.418 - 1.823)

= 0.595 sec.
Fall distance = 1/2 (t²*g)

= 1/2(0.595² x 9.8) = 1.735 metres.  
It is falling.

Its vertical component

= sqrt.(2gh) = sqrt.(19.6 x 1.735m)

= 5.83m/sec.