Question

On seeing enemy ships at a distance of 125 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 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 = 5s, H = 31.25 m

u = 50 m/s, $\theta$ = ${30}^{\circ }$
$\therefore$Time of flight, T = $\frac{2usin\theta }{g}$
= $\frac{2\times 50\times sin{30}^{\circ }}{10}$
= 2 $\times$50$\times$$\frac{1}{2}$$\times$$\frac{1}{10}$
= 5 s
Maximum Height H = $\frac{u^{2}si{n}^2\theta }{2g}$
= $\frac{(50{)}^{2}si{n}^2{30}^{\circ }}{2\left(10\right)}$
= 2500 $\times$$\frac{1}{4}$$\times$$\frac{1}{20}$
= $\frac{2500}{4\times 20}$ = 31.25 m.