Final answer:
The change in the Earth's momentum due to the cart rebounding off a wall is equal in magnitude and opposite in direction to the change in the cart's momentum, adhering to the conservation of momentum in a closed system.
Step-by-step explanation:
The question involves a cart that rebounds off a wall, changing its velocity and therefore its momentum. In the context of conservation of momentum, a closed system (comprising the cart and the Earth in this case) must have a net momentum change of zero. The change in the Earth's momentum is consequently equal in magnitude but opposite in direction to the change in the cart's momentum. If, for example, the cart's mass is m and it changes velocity from +18 m/s (before the collision) to -18 m/s (after bouncing back), the change in momentum of the cart is Δp = m × (final velocity - initial velocity) = m × (-18 m/s - 18 m/s) = -36m (kg·m/s). The Earth's change in momentum will then be +36m (kg·m/s), as it is equal and opposite to the cart's momentum change.