Question

# On seeing enemy ships at a distance of 125√3 m from the shore the cannons start firing fireballs. If the cannons fire at a speed of 50 m/s then at what angle should they aim so they do not miss. Also at what angle can the cannons achieve the maximum distance?

A

Angle to destroy ships = 45°; Angle for maximum range = 90°

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B

Angle to destroy ships = 30°; Angle for maximum range = 45°

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C

Angle to destroy ships = 60°; Angle for maximum range = 45°

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D

Angle to destroy ships = 90°; Angle for maximum range = 90°

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Solution

## The correct options are B Angle to destroy ships = 30°; Angle for maximum range = 45° C Angle to destroy ships = 60°; Angle for maximum range = 45° Range or sx=/125m√3=2×/250020sinθcosθ10 ⇒ sin θ cos θ = √34 cos θ = √32 cos θ = 12 ⇒ θ can be either 30∘ or 60∘ Now to find the maximum distance that the cannon's can hit, we will have to maximize the range of cannons. Range = 2×2500sinθcosθ10 = 250 sin 2θ ( ∵2 sin θ cos θ = sin 2θ) To maximize this we need to maximize sin 2θ We know that is 1 sin 2θ can be maximum 1 When 2θ = 90∘ Or θ = 45∘ So maximum Range = 250m.

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