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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?
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Solution
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
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