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 = u cos α(t)

\[\Rightarrow t = \frac{R}{u\cos\alpha}\]

\[ = \frac{120}{64\cos45^\circ} = 2 . 65 s\]

Vertical distance covered by the football:

\[y = u\text{ sin } \alpha\left( t \right) - \frac{1}{2}g t^2 \]

\[ = 64 \times \frac{1}{\sqrt{2}} \times 2 . 65 - \frac{1}{2} \times 32 . 2 \times \left( 2 . 65 \right)^2\]

 = 6.86 ft < Height of the goalpost
Yes, the football will reach the goalpost