# Elastic Collision In Two Dimensions (Oblique Collision)

Let two body A and B of masses m₁ and m₂ kept on the x-axis. Initially the object B is at rest and A moves toward B with a speed u₁. If the collision is not head on, the object moves along different lines.

Let the object A moves with velocity v₁ making an angle θ with the x-axis and the object B moves with a velocity v₂ making an angle Ø with the same axis.

Let v₁ and v₂ lie in xy-plane, then by using conservation of angular momentum in x and y direction, we get

##### In Y-Direction

Initial momentum in y direction is zero, So

The four unknown quantities cannot be calculated by using the three equation, So if we calculate θ experimentally the value of other three unknown can be solved.

Now, The three casses can be considered as

###### Case-I:- Glancing Collision

In glancing collision, the incident partical does not lose any kinetic energy and is scattered almost undeflected. Thus for each collision θ is nearly equal to zero and Ø=90, then from equation (I) and (II), we get

u₁ = v₁ and v₂ = 0

Kinetic Energy of target particle = 1/2*m₂v₂² = 0

In this type of Collision, the target particle moves in the direction of the incident particle i.e Ø = 0, then from equation (I) and (II) becomes

m₁u₁ =m₁v₁cosθ + m₂v₂ and

0 = m₁v₁sinθ

From equation (III) the Kinetic Energy remains unchanged.

###### Case-III:- Elastic Collision Of Two Identical Particles

In this case,

Hence, We conclude that in a perfectly elastic collision, when a moving particle of mass m colloids elastically in two dimensions with another particle of mass m, after collision the two particle will move at right angle to each other.