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
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
Case-II:- Head-On Collision
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.