A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as 25 g n u 2 , where value of

Question

A particle is projected with velocity u so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as 25 g n u 2 ​ , where value of n is : (Given ' g ' is the acceleration due to gravity).

TestHub · Accepted Answer

​ Range = 3 H m a x ​ g u 2 sin 2 θ ​ = 2 g 3 u 2 sin 2 θ ​ ​ 2 sin θ cos θ = 2 3 ​ sin 2 θ tan θ = 3 4 ​ ⇒ θ = 5 3 ∘ R = g u 2 ( 2 × 5 3 ​ × 5 4 ​ ) ​ ⇒ 25 g 24 u 2 ​

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