Q. A coastguard ship locates a pirate ship at a distance $560\ m$. It fires a cannon ball with an initial speed $82\ m/s$. At what angle from horizontal the ball must be fired so that it hits the pirate ship
A) $54{^\circ}$
B) $125{^\circ}$
C) $27{^\circ}$
D) $18{^\circ}$
Explanation
(c) Horizontal range $R = \frac{u^{2}\sin{2\theta}}{g}$
Substituting the given values we get
$560 = \frac{82 \times 82 \times \sin{2\theta}}{9.8}$
$\Rightarrow \sin{2\theta} = \frac{560 \times 9.8}{82 \times 82} = \frac{5488}{6724}$
$\Rightarrow \sin{2\theta} = 0.82\ \Rightarrow 2\theta = \sin^{- 1}(0.82)$
$\Rightarrow 2\theta = 55.1{^\circ} \Rightarrow \theta \approx 27{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.