The maximum height attained by a projectile when thrown at an angle θ with the horizontal is found to be half the horizontal range. Then θ is equal to

Question

The maximum height attained by a projectile when thrown at an angle θ with the horizontal is found to be half the horizontal range. Then θ is equal to, tan - 1 2, π 6, π 4, tan - 1 1 2

MARKS App · Accepted Answer

Maximum height, H ⁡ 0 = u 2 sin 2 θ 2 g Range, R ⁡ = u 2 sin 2 θ g = 2 u 2 sin θ cos θ g Given, H 0 = R 2 ∴ u 2 sin 2 θ 2 g = 2 u 2 sin θ cos θ 2 g ⇒ sin θ = 2 cos θ ⇒ tan θ = 2 ∴ θ = tan - 1 2

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