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.
Answer:
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
