Question

The maximum range of a gun on a horizontal terrain is $16\text{km}$. If $g=10{\text{m/s}}^2$, then muzzle velocity of the shell must be

• A. $160\text{m/s}$
• B. $200\sqrt{2}\text{m/s}$
• C. $400\text{m/s}$
• D. $800\text{m/s}$

Answer 1

The correct option is C $400\text{m/s}$

We know,
$R=\frac{u^2\sin 2\theta }{g}$
For maximum range $\theta ={45}^{\circ }$

$R_{max}=\frac{u^2}{g}$
$u=\sqrt{R_{max}\times g}u=\sqrt{16\times {10}^3\times 10}\Rightarrow u=400m/s$