Assuming that the second particle is at rest before the collision, the angles of deflection of the two particles, θ θ 1 and θ θ 2 , are related to the angle of deflection θ θ in the system of the center of mass by tan ⁡ ⁡ θ θ 1 = m 2 sin ⁡ ⁡ θ θ m 1 + m 2 cos ⁡ ⁡ θ θ , θ θ 2 = π π − − θ θ 2 . The magnitudes of the velocities of the particles after the collision are: v 1 ′ = v 1 m 1 2 + m 2 2 + 2 m 1 m 2 cos ⁡ ⁡ θ θ m 1 + m 2 v 2 ′ = v 1 2 m 1 m 1 + m 2 sin ⁡ ⁡ θ θ 2 .