Assume that bullet P is fired from a gun when the angle of elevation of the gun 30o. Another bullet Q is fired from the gun when the angle of elevation is 60o. if the vertical height attained
in the second case is ‘x’ times the vertical height attained in the first case, find the value of ‘x’

Answer :

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Given : The bullet P is fired from a gun when the angle of elevation of the gun 30°. Another bullet Q is fired from the gun when the angle of elevation is 60°. if the vertical height attained

in the second case is ‘x’ times the vertical height attained in the first case.

To find : The value of x.

solution : it is based on concept of projectile motion.

we know, vertical height, H = u²sin²θ/2g

when angle of elevation is 30° .

H₁ = u²sin²30°/2g .......(1)

when angle of elevation is 60°.

H₂ = u²sin²60°/2g .......(2)

as it is given that, H₂ = x H₁

⇒u²sin²60°/2g = x × u²sin²30°/2g

⇒sin²60° = x × sin²30°

⇒(√3/2)² = x × (1/2)²

⇒3/4 = x/4

⇒x = 3

Therefore the value of x must be 3.

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