Question

A football player kicks a ball at distance 10m from a vertical pole at an angle 45. The ball just clears the tip of the pole and falls at a distance 10m on the other side. Determine the height of the pole

Answer 1

Answer:

Since the ball just clears the tip of the pole, the height of the pole is the maximum height of the projectile. Thus the pole was of height 5 metres.

The height of the pole is h=2.4m

Explanation:

A body A exerts a force on another body B, and B responds by exerting an equal and opposite force on A. This is known as Newton's third rule. As a result, when kicking a ball, a footballer's leg will feel force on par with the force applied to the ball, but in the opposite direction.

A football moves in the direction of the force exerted when it is kicked by a player. In addition, the football player feels a force on his leg that is equivalent to the power he applied to the ball.

$\begin{aligned}& \mathrm{R}=\frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{g}}=10 \mathrm{~m} \\& \mathrm{u}^2 \sin 90=100 \\& \mathrm{u}^2=100 \\& \mathrm{u}=10 \mathrm{~m} / \mathrm{s} \\& \mathrm{H}=\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}} \\& =\frac{100 \times \sin ^2\left(45^{\circ}\right)}{20} \\& =5 \times \frac{1}{2}=2.5 \mathrm{~m}\end{aligned}$

Motion in the horizontal direction:

$\begin{aligned}& u \cos 45 \times t=4 \\& \Longrightarrow \mathrm{t}=2 \sqrt{2} / 5\end{aligned}$

Motion in the Vertical Direction :

$h=u \sin 45-\mathrm{gt}^2 / 2$

$\Longrightarrow \mathrm{h}=2.4 \mathrm{~m}$

∴The height of the pole is h=2.4m

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