A 4.0-kg ball with a velocity of in the collides head-on elastically with a stationary 2.0-kg ball. What are the velocities of the balls after the collision

Complete question:

4.0 kg ball with a velocity of 4 m/s in the +x-direction collides head-on elastically with a stationary 2.0-kg ball. What are the velocities of the balls after the collision.

The final velocity of the first is 1.33 m/s

The final velocity of the second ball is 5.33 m/s

Explanation:

Given;

mass of the first ball, m₁ = 4.0 kg

mass of the second ball, m₂ = 2.0 kg

initial velocity of the first ball, u₁ = 4 m/s

initial velocity of the second ball, u₂ = 0

let the final velocity of the first ball after collision = v₁

also, let the final velocity of the second ball after collision = v₂

Apply the principle of conservation of linear momentum;

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

4(4) + 0 = 4v₁ + 2v₂

16 = 4v₁ + 2v₂

8 = 2v₁ + v₂ equation (1)

Apply one-directional velocity;

u₁ + v₁ = u₂ + v₂

4 + v₁ = 0 + v₂

4 + v₁ = v₂ equation (2)

Substitute in equation (2) into equation (1)

8 = 2v₁ + v₂

8 = 2v₁ + (4 + v₁)

8 = 2v₁ + 4 + v₁

8 - 4 = 2v₁ + v₁

4 = 3v₁

v₁ = 4 / 3

v₁ = 1.33 m/s

Then, v₂ = 4 + v₁

v₂ = 4 + 1.33

v₂ = 5.33 m/s

b.

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