To solve this problem, we can apply the principle of conservation of momentum. The total momentum before the explosion should be equal to the total momentum after the explosion.
The initial momentum of the system before the explosion is given by the product of the mass and velocity of the box:
Initial momentum = (mass of the box) * (velocity of the box) = 6 kg * 4 m/s = 24 kg·m/s
After the explosion, we have two pieces. Let's call the velocity of the second piece (with mass 4 kg) v₂.
The momentum of the first piece (2 kg) after the explosion is given by:
Momentum of the first piece = (mass of the first piece) * (velocity of the first piece) = 2 kg * 8 m/s = 16 kg·m/s
The momentum of the second piece (4 kg) after the explosion is given by:
Momentum of the second piece = (mass of the second piece) * (velocity of the second piece) = 4 kg * v₂
According to the principle of conservation of momentum, the total momentum after the explosion should be equal to the initial momentum:
Total momentum after the explosion = Initial momentum
Momentum of the first piece + Momentum of the second piece = Initial momentum
16 kg·m/s + 4 kg * v₂ = 24 kg·m/s
Simplifying the equation:
4 kg * v₂ = 24 kg·m/s - 16 kg·m/s = 8 kg·m/s
Dividing both sides by 4 kg:
v₂ = 8 kg·m/s / 4 kg = 2 m/s
Therefore, the velocity of the second piece is 2 m/s.