Question

To win the game, a place kicker must kick a

football from a point 24 m (26.2464 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 17 m/s at
an angle of 53.2° from the horizontal.
The acceleration of gravity is 9.8 m/s?.
By how much vertical distance does the ball
clear the crossbar?
Answer in units of m.

Answer 1

1.85 m

Step-by-step explanation:

We can start by calculating how much time takes the ball to cover the horizontal distance that separates the starting point from the crossbar, which is

d = 24 m

The horizontal velocity of the ball is constant and it is

`v_x = u cos \theta = (17)(cos 53.2^(\circ))=10.2 m/s`

So the time taken to cover the horizontal distance d is

`t=(d)/(v_x)=(24)/(10.2)=2.35 s`

Now we can analyze the vertical motion of the ball. The vertical position of the ball at time t is given by

`y(t) = u_y t - (1)/(2)gt^2`

where

`u_y = u sin \theta = (17)(sin 53.2^(\circ))=13.6 m/s` is the initial vertical velocity

g = 9.8 m/s^2 is the acceleration of gravity

Substituting t = 2.35 s, we find the vertical position of the ball when it is passing above the crossbar:

`y=(13.6)(2.35)-(1)/(2)(9.8)(2.35)^2=4.90 m`

And since the height of the crossbar is

h = 3.05 m

The ball passes

`\Delta h = 4.90 - 3.05 = 1.85 m` above the crossbar.