The trajectory of a projectile in a vertical plane is y = α x - β x 2 , where α and β are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of

Question

The trajectory of a projectile in a vertical plane is y = α x - β x 2 , where α and β are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by

TestHub · Accepted Answer

y = α x - β x 2 comparing with trajectory equation y = x tan θ - 1 2 g x 2 u 2 cos 2 θ tan θ = α ⇒ θ = tan - 1 α β = 1 2 g u 2 cos 2 θ u 2 = g 2 β cos 2 θ Maximum height : H H = u 2 sin 2 θ 2 g = g 2 β cos 2 θ sin 2 θ 2 g H = tan 2 θ 4 β = α 2 4 β

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