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)

$20\, cm$

Answer 2

$R=\frac{u^{2}\,sin\,2\theta}{g} ; h_{max}=\frac{u^{2}\,sin^{2}\,\theta}{2g}$ 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 $20\,cm$