Question

In a soccer practice session the ball is kept at the centre of the field $40$ yards from the $10ft$ high goal post . A goal is attempted by kicking the ball at a speed of $64ft/s$ at an angle of ${45}^0$ to the horizontal. Will the ball reach the goal post ?

Answer 1

The acceleration due to gravity on earth is $g=9.8m/s^2$

We know that $40yards=120feet$

Horizontal range $x=120ft$

The initial speed of the ball is $u=64ft/s$

The angle at which the ball is kicked $\theta$=${45}^0$

know that horizontal range $x=ucos\theta t$

t=$\frac{x}{ucos\theta }$

t=$\frac{120}{64cos{45}^0}$

t=$\frac{120}{64\times \frac{1}{\sqrt{2}}}$

=$\frac{120\times 1.414}{64}$

=$2.65sec$

y=$\frac{sin\theta \left(t\right)-1}{2g{t}^2}$

=$\frac{sin\left(45\right)\times 2.65-1}{2\times \left(32.2\right)\times (2.65{)}^2}$=7.08 ft which is less than the eight of goal post.

in time 2.65 sec the ball travels a horizontal distance of 120 ft and vertical height 7.08 ft which is less than 10 ft.

hence, the ball will reach the post.