Question

The maximum range of a gun or horizontal range is 16 km. If g = 10 ${ms}^{-1}$. The muzzle velocity of the shell must be:-

• A. $1600{ms}^{-1}$
• B. $400{ms}^{-1}$
• C. $200\sqrt{2}{ms}^{-1}$
• D. $160\sqrt{10}{ms}^{-1}$

Answer 1

The correct option is B $400{ms}^{-1}$

Horizontal Range $R=\frac{u^2\sin 2\theta }{g}$

For maximum horizontal range $\theta ={45}^0$

or$,$ $R^{max}=\frac{u^2}{g};$ where $u$ is the muzzle velocity of the shell

$\therefore 1600m=\frac{u^2}{10m/s^2}$

$\therefore u=400m/s$

Hence,

option $\left(B\right)$ is correct answer.