1. Object at Rest Explodes

* Conservation of Momentum: The key principle here is the conservation of momentum. Momentum is a measure of mass in motion. In a closed system (like an explosion), the total momentum before the event must equal the total momentum after the event.

* Initial Momentum: Since the object is at rest initially, its total momentum is zero.

* Final Momentum: After the explosion, the two parts will have equal and opposite momenta to ensure the total momentum remains zero.

* Conclusion: The two parts do *not* necessarily move in exactly opposite directions. Their directions will depend on the masses and velocities of the two parts. However, they will have momenta that are equal and opposite.

2. Moving Object Strikes Stationary Object

* Conservation of Momentum: Again, momentum is conserved.

* Initial Momentum: The moving object has momentum, and the stationary object has zero momentum.

* Final Momentum: After the collision, the objects will move off with a combined momentum equal to the initial momentum of the moving object.

* Conclusion: The objects will not necessarily move in exactly opposite directions. Their directions will depend on the masses and velocities involved in the collision.

Example:

Imagine a bomb at rest explodes into two pieces. If one piece is much heavier than the other, the heavier piece will move slower and in a direction opposite to the lighter piece. This ensures the total momentum (mass times velocity) is equal and opposite for both pieces.

Key Point: While the directions of the objects may not be exactly opposite, the *momenta* of the objects will always be equal and opposite to maintain conservation of momentum.