Final answer:
The question addresses the conservation of momentum in physics, specifically involving a scenario where Carmen leaves a canoe causing it and Judi to move in the opposite direction. By applying the principle and given masses and speeds, the speed and direction of the canoe and Judi can be calculated.
Step-by-step explanation:
The question involves the principle of conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces are applied. The situation describes Carmen leaving a canoe at a certain speed and seeking to find out the speed at which the canoe and Judi will move after Carmen has exited.
To solve this, we can set the initial momentum of the system to be equal to the final momentum. Since the canoe and its occupants are initially at rest, their combined initial momentum is zero. When Carmen exits the canoe, her momentum must be balanced by the momentum of the canoe and Judi moving in the opposite direction.
We can express this using the formula:
Momentum of Carmen = - (Momentum of canoe and Judi)
(Carmen's mass) × (Carmen's velocity) = - ((Canoe and Judi's combined mass) × (Their velocity))
Using the given values: (80.0 kg) × (4.0 m/s) = - ((115 kg) × (velocity of canoe and Judi))
The resulting velocity of the canoe and Judi can be found by dividing the momentum of Carmen by the combined mass of Judi and the canoe. This will give the speed of the canoe and Judi moving in the opposite direction to Carmen's original movement.