Answer :
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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