Question

A boy aims at a bird from a point at a horizontal distance of $100m$. The gun can impart a velocity of $500m/s$ to the bullet. At what height above the bird must he aim his gun in order to hit? $(g=10m/s^2)$.

• A. $20cm$
• B. $40cm$
• C. $50cm$
• D. $100cm$

Answer 1

Answer: (A)

$R=\frac{u^{2}sin2\theta }{g};h_{max}=\frac{u^{2}si{n}^2\theta }{2g}$

Given $u=500m/s$;
$\frac{R}{2}=100$
$\Rightarrow R=200m$
$sin2\theta =\frac{Rg}{u^2}$
$\Rightarrow \frac{200\times 10}{500^2}$
$\Rightarrow 2\theta =0.4583$
$\theta =0.2291$
$\Rightarrow \theta =0.23$ degrees
$\Rightarrow H=\frac{500^{2}si{n}^{2}0.23}{2g}$
$=0.20m$ or $20cm$