Question

To win the game, a placekicker must kick a football from a point 44 m (48.1184 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 24 m/s at an angle of 31◦
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

Answer:

The distance by the ball clear the crossbar is 1.15 m

Explanation:

Given that,

Distance = 44 m

Speed = 24 m/s

Angle = 31°

Height = 3.05 m

We need to calculate the horizontal velocity

Using formula of horizontal velocity

$u_{x}=u\cos\theta$

Put the value into the formula

$u_{x}=24\cos(31)$

$u_{x}=20.5\ m/s$

We need to calculate the vertical velocity

Using formula of vertical velocity

$u_{y}=u\sin\theta$

Put the value into the formula

$u_{y}=24\sin(31)$

$u_{y}=12.3\ m/s$

We need to calculate the time

Using formula of time

$t=\dfrac{d}{u_{x}}$

Put the value into the formula

$t=\dfrac{44}{20.5}$

$t=2.1\ sec$

We need to calculate the vertical height

Using equation of motion

$h=u_{y}t+\dfrac{1}{2}at^2$

Put the value into the formula

$h=12.3\times2.1-\dfrac{1}{2}\times9.8\times(2.1)^2$

$h=4.2\ m$

We need to calculate the distance by the ball clear the crossbar

Using formula for vertical distance

$d=h-3.05$

Put the value of h

$d=4.2-3.05$

$d=1.15\ m$

Hence, The distance by the ball clear the crossbar is 1.15 m