Question

In a soccer practice session the football is kept at the centre of the filed 40 yards from the 10 ft high goalposts. A goal is attempted by kicking the football at a speed of 64 ft/s at an angle of 45° to the horizontal. Will the ball reach the goal post?

Answer 1

Given:
Height of the goalpost = 10 ft
The football is kept at a distance of 40 yards, i.e., 120 ft, from the goalpost.
Initial speed u with which the ball is hit = 64 ft/s
Acceleration due to gravity, a = g = 9.8 m/s² = 32.2 ft/s²
For the given question, 40 yards is the horizontal range (R).
Angle of projection, α = 45°
We know that the horizontal range is given by
R = ucosα(t)
$$\begin{gathered} \Rightarrow t=\frac{R}{u\cos \alpha } \\ =\frac{120}{64\cos 45°}=2.65\mathrm{s} \end{gathered}$$

Vertical distance covered by the football:
$$\begin{gathered} y=u\mathrm{sin\alpha }\left(t\right)-\frac{1}{2}g{t}^2 \\ =64\times \frac{1}{\sqrt{2}}\times 2.65-\frac{1}{2}\times 32.2\times {\left(2.65\right)}^2 \end{gathered}$$
= 6.86 ft < Height of the goalpost
Yes, the football will reach the goalpost.