Final answer:
The speed of the 2-kg box after the explosion can be calculated using the principle of conservation of momentum, but the question does not provide enough information to determine the exact speed.
Step-by-step explanation:
The speed of the 2-kg box after the explosion can be determined using the principle of conservation of momentum. The initial momentum of the system is zero since the boxes were at rest. After the explosion, the momentum of the 2-kg box will be equal in magnitude but opposite in direction to the momentum of the other box. Therefore, the speed of the 2-kg box can be calculated by dividing the magnitude of the momentum of the other box by its mass.
Mathematically, this can be expressed as:
v = p/m
where v is the speed of the 2-kg box, p is the momentum of the other box, and m is the mass of the other box.
Since the question does not provide the momentum of the other box or its mass, it is not possible to determine the exact speed of the 2-kg box without further information.