Question

A person aims a gun at a bird from a point at horizontal distance of $100m$. If gun can impact a speed of $500m{s}^{-1}$ to the bullet. At what height above the bird must he aim his gun in order to hit it?$(g=10m{s}^{-2})$

• A. $10.4cm$
• B. $20.35cm$
• C. $50cm$
• D. $100cm$

Answer 1

Answer: (B)

$20.35cm$

Let the gun be fired with velocity $u$ from point $O$ on the bird at $B,$ making angle $\theta$ with the horizontal or direction. Therefore the height of the aims of the person is at height $BA(=h)$ above the bird.
Here, $Horizontalrange=\frac{u^2\sin 2\theta }{g}=100$
$\frac{{500}^2\sin 2\theta }{10}=100$

$\sin 2\theta =\frac{100\times 10}{(500{)}^2}=\frac{1}{250}$

$2\theta ={14}^{\prime }or\theta =7^{{}^{\prime }}=\frac{7}{60}\times \frac{\pi }{180}radian$

As $angle=\frac{arc}{radius}$

$\therefore \theta =\frac{AB}{OB}$

or $AB=\theta \times OB$

$AB=\frac{7}{60}\times \frac{\pi }{180}\times (100\times 100)cm=20.35cm$