An inclined plane makes an angle α with the horizontal. A particle is projected from a point on the plane at an angle θ with the horizontal, where θ > α, and strikes the inclined plane again perpendicularly. Which relation between θ and α is correct?
Options

Question

An inclined plane makes an angle α with the horizontal. A particle is projected from a point on the plane at an angle θ with the horizontal, where θ > α, and strikes the inclined plane again perpendicularly. Which relation between θ and α is correct?

Options

G1 Physics · Accepted Answer

At impact, for the velocity to be perpendicular to the inclined plane, its component along the plane must be zero: vₓcosα + vᵧsinα = 0. Here vₓ = ucosθ and vᵧ = usinθ - gt. The time to hit the plane is T = 2u sin(θ - α)/(g cosα). Substituting T into the perpendicular-impact condition and simplifying gives 2 tanα · tan(θ - α) = 1. Therefore tan(θ - α) = 1/(2 tanα). Hence option B is correct.

An inclined plane makes an angle α with the horizontal. A particle is projected from a point on the plane at an angle θ with the horizontal, where θ &gt; α, and strikes the inclined plane again perpendicularly. Which relation between θ and α is correct?

An inclined plane makes an angle α with the horizontal. A particle is projected from a point on the plane at an angle θ with the horizontal, where θ > α, and strikes the inclined plane again perpendicularly. Which relation between θ and α is correct?