In order to win the game of football, player has to kick the ball at a distance of 45 m from the goal which must cross the bar at 3.05 m of height. The vertical distance by which the ball clears the cross bar is 1.65 metres.
Answer: 1.65 metre
Explanation:
Given, velocity = 24 m/s, angle of projectile= 32.6 degrees and acceleration = 9.8 [tex]m / s^{2}[/tex]
To know the height, we first need to know the velocity component,
[tex]v_{x}=24 \sin 32.6^{\circ}=12.9 \mathrm{m} / \mathrm{s}[/tex]
[tex]v_{y}=24 \cos 32.6^{\circ}=20.2 \mathrm{m} / \mathrm{s}[/tex]
The time travelled by the ball = [tex]\frac{\text { distance travelled }}{\text {velocity in the direction of travel}}=\frac{45}{20.2}=2.2 \mathrm{sec}[/tex]
From the equation of motion,
[tex]s_{y} = v_{y} t+\frac{1}{2} a t^{2}[/tex]
= [tex]12.9 \times 2.2+\frac{1}{2}-9.8 \times 2.2 \times 2.2[/tex]
[tex]s_{y}[/tex] = 4.7 m.
Therefore, the vertical distance by which all ball clears the cross bar = ball height – cross bar height = 4.7 – 3.05 = 1.65 metre.
