Question

On seeing enemy ships at a distance of $125\text{m}$ from the shore, the canons start firing fireballs. The captain of the ship saw the cannon fire. He knows the velocity of the fireballs is $50\text{m/s}$. Now in how much time does he have to steer his ship in some other direction so as to save his crew. Use angle of projection as ${30}^{\circ }$. Also find the maximum height that the fireball reaches above water.

• A. T = 5s, H = 31.25 m
• B. T = 5s, H = 45.6 m
• C. T = 11s, H = 31.25 m
• D. T = 10s, H = 45.1 m

Answer 1

The correct option is A

$T=5\text{s},H=31.25\text{m}$

$u=50\text{m/s},\theta ={30}^{\circ }$
$\therefore$Time of flight, $T=\frac{2u\sin \theta }{g}$
$T=\frac{2\times 50\times \sin {30}^{\circ }}{10}$
$T=2\times 50\times$$\frac{1}{2}$$\times$$\frac{1}{10}$
$T=5\text{s}$

Maximum Height $H=\frac{u^2{\sin }^2\theta }{2g}$
$H=\frac{(50{)}^2{\sin }^2{30}^{\circ }}{2\left(10\right)}$

$H=2500\times$$\frac{1}{4}$$\times$$\frac{1}{20}$

$H=\frac{2500}{4\times 20}=31.25\text{m}$

Hence, option $\left(\text{A}\right)$ is the right choice.