Question

Galileo writes that for angles of projection of a projectile at angles (45⁰+ θ) and (45⁰ - θ) , the horizontal ranges described by the projectile are in the ratio of (if θ ≤ 45⁰ )

Moderate

Solution

R = u²/g sin2α = u²/g sin (π - 2α) = u²/g sin2(π/2 - α)
⇒ R = u²/g sin2α = u²/g sin 2ß
Where ß = π/2 - α = Another angle of projection which produces the same range.
Here α + ß = π/2
If α =(45⁰ +θ) , ß must be equal to (45⁰ - θ)
.: Option - (3) is right.

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