College Physics

Question

To win the game, a place kicker must kick a
football from a point 28 m (30.6208 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 18 m/s at
an angle of 44.4
◦
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

Calculate how long it takes to cross 28 m in the horizontal direction, plug that time into the height equation, and evaluate the difference of the two heights.

 

t = x/v_x = [28 / (18cos44.4°)] s = ? s

 

Plug this value of t into

 

h(t) = -4.9t² + (18sin44.4°)t

 

Finally, evaluate

 

h(t) - (3.05 m) = ? m

 

The result must be ≥ 0.  Otherwise, the ball will not clear the crossbar.