Question

The horizontal range of a bullet fired at ${45}^{\circ }$ is $1000\text{m}$. If it is fired from the lorry, in the direction of lorry's motion, which is moving at $10\text{m/s}$, with the same velocity and elevation, then find its range in metre (Take $g=10{\text{m/s}}^2$)
Take $\sqrt{2}=1.414$.

Answer 1

Range $=\frac{u^2\sin 2\theta }{g}$
$\Rightarrow 1000=\frac{u^2}{10}$
$\Rightarrow u=100\text{m/s}$
Time of flight $=\frac{2u\sin \theta }{g}$
$=\frac{2\times 100\times \frac{1}{\sqrt{2}}}{10}$
$=10\sqrt{2}\text{sec}$
Extra Range = (Velocity of lorry) $\times$ time
$=10\times 10\sqrt{2}$
$=141.42\text{m}$
Total Range $=1141.42\text{m}$