Answer:
Explanation:
When the camper steps onto the dock, the canoe and the other camper will move in the opposite direction to conserve momentum.
To find the speed and direction of the canoe and the other camper, we can use the principle of conservation of momentum. The initial momentum of the system (camper + canoe) should be equal to the final momentum of the system.
Given:
- Mass of the camper who steps onto the dock = 75.0 kg
- Initial velocity of the camper who steps onto the dock = 3.8 m/s
- Combined mass of the canoe and the other camper = 115 kg
Let's calculate the initial momentum (P_initial) of the system using the formula:
P_initial = mass × velocity
P_initial = (75.0 kg + 115 kg) × 3.8 m/s
P_initial = 190 kg × 3.8 m/s
P_initial = 722 kg·m/s
According to the conservation of momentum, the final momentum (P_final) of the system should also be 722 kg·m/s.
Since the camper who steps onto the dock comes to rest on the dock, the final velocity of the camper is 0 m/s. Let's assume the final velocity of the canoe and the other camper is V.
P_final = (mass of canoe + mass of other camper) × V
722 kg·m/s = (115 kg) × V
V = 722 kg·m/s / 115 kg
V ≈ 6.28 m/s
Therefore, the canoe and the other camper will move in the opposite direction with a speed of approximately 6.28 m/s. The direction of their movement will be opposite to the direction in which the camper initially moved, as per the conservation of momentum principle.
