The velocity of the red cart after the collision is 2 m/s
From the law of conservation of momentum, initial momentum of system = final momentum of system.
m₁v₁ + m₂v₂ = m₁v₃ + m₂v₄ where m₁ = mass of red cart = 4 kg, v₁ = velocity of red cart before collision = + 4 m/s, v₃ = velocity of red cart after collision, m₂ = mass of blue cart = 1 kg, v₂ = velocity of blue cart before collision = 0 m/s (since it is initially at rest) and v₄ = velocity of blue cart after collision = + 8 m/s.
Substituting the values of the variables into the equation, we have,
m₁v₁ + m₂v₂ = m₁v₃ + m₂v₄
4 kg × 4 m/s + 1 kg × 0 m/s = 4v₃ + 1 kg × 8 m/s
16 kgm/s + 0 kgm/s = 4v₃ + 8 kgm/s
16 kgm/s = 4v₃ + 8 kgm/s
16 kgm/s - 8 kgm/s = (4 kg)v₃
(4 kg)v₃ = 8 kgm/s
Divide both sides by 4 kg, we have
v₃ = 8 kgm/s ÷ 4 kg
v₃ = 2 m/s
The velocity of the red cart after the collision is 2 m/s.
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