Question

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

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

Answer 1

Answer: (A)

$R=\frac{u^{2}\,sin\,2\theta}{g} ; h_{max}=\frac{u^{2}\,sin^{2}\,\theta}{2g}$

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