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 24.0 m/s at an angle of 51.0° to the horizontal.

Question

(a) By how much does the ball clear or fall short of clearing the crossbar? (Enter a negative answer if it falls short.)
m
(b) Does the ball approach the crossbar while still rising or while falling?
rising
falling

Answer 1

u = horizontal speed forever = 24 cos 51 = 15.1 m/s
v = vertical speed = 24 sin 51 - 9.81 t = 18.7 - 9.81 t
x = horizontal distance = 15.1 t
y = height = 18.7 t - 4.9 t^2
so
a)
time at crossbar = 36.0 / 15.1 = 2.38 seconds
height at crossbar = 18.7 (2.38) - 4.9 (2.38)^2 = 44.5 - 27.8 = 16.7 meters
so 16.7 - 3.05

Answer 2

b) when is the vertical speed = 0?
v= 18.7 -9.81 t
so t at top = 1.9 seconds
but it takes 2.38 seconds to reach crossbar
so it is on the way down