Notes

Collision in Two-Dimensions…

Collision in Two-Dimensions – Oblique collision The collision after which the direction of velocity of bodies make some angle with the direction of velocities of body before the collision is known as oblique collision. Consider two objects, P of mass m₁. Moving with speed u along X – axis and Q of mass m₂ at rest. Suppose, the collision is oblique (not head – on) and m₁ moves with velocity v₁ at angle θ and m₂ with velocity v₂ at any angle ɸ as shown below. In this type of collision, we resolve the velocities in two mutually perpendicular axes.

From conservation of linear momentum, (p_x)_i = (p_x)_f ⇒ m₁u = (m₁ + m₂)v_x = m₁v₁cosθ + m₂v₂cos ɸ (p_y)_i = (p_y)_f ⇒ 0 = m₁v₁sinθ – m₂v₂sin ɸ ⇒ v₁sinθ = v₂sin ɸ

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