Question

A bullet is fired from a cannon with velocity $500$ $m/s$. If the angle of projection is ${15}^o$ and $g=10$ $m{s}^{-2}$, then the range is :

• A. $25\times {10}^{3}m$
• B. $12.5\times {10}^{3}m$
• C. $50\times {10}^{2}m$
• D. $25\times {10}^{2}m$

Answer 1

The correct option is B $12.5\times {10}^{3}m$

$\text{Step 1: Range of the projectile [Refer Fig.]}$

Range is given by:

$R=\frac{u^2\sin 2\theta }{g}$ $(\theta =\text{Angle of projection, u = Initial speed})$

$\text{Step 2: Substituting values}$

$R=\frac{\left(500m/s{)}^2\sin \right(2\times {15}^o)}{10m/s^2}$$=12500m$

$R=12.5\times {10}^{3}m$

Hence the range is $12.5\times {10}^{3}m$.

Option $B$ is correct.