To win the game, a place kicker must kick a

Question

football from a point 54 m (59.0544 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 26 m/s at
an angle of 33.8
◦
from the horizontal.
The acceleration of gravity is 9.8 m/s
2
.
By how much vertical distance does the ball
clear the crossbar?
Answer in units of m.

Answer 1

The ball's initial horizontal speed is 26*cos(30.6) m/s and there is no horizontal acceleration.
The ball's initial vertical speed is 26*sin(30.6) m/s and there is a vertical acceleration of -g

Resolving horizontally to find the time it takes to reach the crossbar:
s = ut + a(t^2)/2
52 = 26*cos(30.6)*t
t = 52/(26*cos(30.6)) = 2.324 seconds

Resolving vertically to calculate the height of the ball at the time it is passing the crossbar:
s = ut + a(t^2)/2
s = 26*sin(30.6)*t - (g/2)*(t^2)
s = 4.271 Meters

So the ball clears the post at a height of 1.221 Meters.