Question

The maximum range of a gun on horizontal plane is 16 km. If g = 10ms^-2 , then muzzle velocity of a shell is

• A. 160 ms^-1
• B. 200$\sqrt2$ ms^-1
• C. 400 ms^-1
• D. 800 ms^-1

Answer 1

The Correct Option is C

The maximum range of a projectile on a horizontal plane is given by the formula:

$R_\text{max} = \frac{u^2}{g}$

where:

• $R_\text{max}$ is the maximum range,
• $u$ is the initial velocity (muzzle velocity in this case), and
• $g$ is the acceleration due to gravity.

We are given $R_\text{max} = 16\,\text{km} = 16000\,\text{m}$ and $g = 10\,\text{m/s}^2$. We need to find $u$.

Rearranging the formula to solve for $u$:

$u = \sqrt{R_\text{max} \cdot g}$

Substituting the given values:

$u = \sqrt{16000\,\text{m} \times 10\,\text{m/s}^2} = \sqrt{160000\,\text{m}^2/\text{s}^2} = 400\,\text{m/s}$

The correct answer is (C) 400 ms^-1.