A coastguard ship locates a pirate ship at a distance 560 m. It fires a cannon ball with an initial speed 82 ms-1 . At what angle from horizontal the ball must be fired so that it hits the pirate ship?

Question

A coastguard ship locates a pirate ship at a distance 560 m. It fires a cannon ball with an initial speed 82 ms-1 . At what angle from horizontal the ball must be fired so that it hits the pirate ship? (A)  54°  (B)  125°  (C)  27°  (D)  18°

Tardigrade Admin · Accepted Answer

Range =(u2 sin 2 θ/g) ∴ 560=((82)2 sin 2 θ/10) or sin 2 θ=0.832[ sin 56.30°=0.832] ⇒ θ ≈ 27°

Q. A coastguard ship locates a pirate ship at a distance $560 m$ . It fires a cannon ball with an initial speed $82 m s^{- 1}$ . At what angle from horizontal the ball must be fired so that it hits the pirate ship?

$5 4^{\circ}$

$12 5^{\circ}$

$2 7^{\circ}$

$1 8^{\circ}$

Range $= \frac{u ^{2} s i n 2 θ}{g}$
$∴ 560 = \frac{( 82 ) ^{2} s i n 2 θ}{10}$
or $sin 2 θ = 0.832 [sin 56.3 0^{\circ} = 0.832]$
$\Rightarrow θ \approx 2 7^{\circ}$

Q. A coastguard ship locates a pirate ship at a distance 560m. It fires a cannon ball with an initial speed 82ms−1 . At what angle from horizontal the ball must be fired so that it hits the pirate ship?

54∘

125∘

27∘

18∘