A smooth steel ball strikes a fixed smooth steel plate at an angle θ with the vertical. If the coefficient of restitution is e , the angle at which the re-bounce will take place is

Step-by-step solution

Since, no force is present along the surface of plate. So, momentum conservation principle for ball is applicable along the surface of plate. m υ sin ⁡ θ 1 = m υ sin ⁡ θ 2 Or υ sin ⁡ θ 1 = υ 1 sin ⁡ θ 2 …(i) e = υ 1 cos ⁡ θ 2 υ cos ⁡ θ 1 = υ 1 cos ⁡ θ 2 υ cos ⁡ θ ( θ 1 = θ ) ∴ υ 1 cos ⁡ θ 2 = e υ cos ⁡ θ …(ii) ∴ υ 1 sin ⁡ θ 2 υ 1 cos ⁡ θ 2 = υ sin ⁡ θ e υ cos ⁡ θ = tan ⁡ θ e ∴ tan ⁡ θ 2 = tan ⁡ θ e ∴ θ 2 = tan - 1 ⁡ tan ⁡ θ e