A projectile is projected with velocity of 40 m / s at an angle θ with the horizontal. If R be the horizontal range covered by the projectile and after t seconds, its inclination with horizontal becom

Question

A projectile is projected with velocity of 40 m / s at an angle θ with the horizontal. If R be the horizontal range covered by the projectile and after t seconds, its inclination with horizontal becomes zero, then the value of cot θ is [Take, g = 10 m / s 2 ]

TestHub · Accepted Answer

At maximum height, inclination with horizontal becomes zero. Time (taken by) projectile to reach maximum height, t ⇒ u ​ = g u sin θ ​ = sin θ g t ​ … ( i ) ​ Since, R = u cos θ × ( 2 t ) ⇒ cos θ ⇒ cos θ ​ = 2 u t R ​ = 2 ⋅ s i n θ g t ​ ⋅ t R ​ = 2 g t 2 R sin θ ​ ( U s in g ( i )) ​ ⇒ cot θ = 2 g t 2 R ​ = 2 × 10 t 2 R ​ = 20 t 2 R ​

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