A 30-kg child stands at one end of a floating 20-kg canoe that is 5.0-m long and initially at rest in the water.The child then slowly walks to the other end of the canoe.How far does the canoe move in the water,assuming water friction is negligible?
A)1.0 m
B)2.0 m
C)3.0 m
D)4.0 m
E)5.0 m

Question

Quizplus · Accepted Answer

According to the principle of conservation of momentum, when the child starts moving towards the other end, the total momentum of the system (child and canoe) must remain constant. Since the initial momentum is zero, the final momentum must also be zero. This means that the canoe must move in the opposite direction to compensate for the child's motion.

The child moves from one end to the other end, covering a distance of 5.0 m. Since the canoe is initially at rest, the center of mass of the system (child and canoe) is at rest. When the child moves to the other end, the center of mass of the system is displaced by a distance of 2.5 m (half the length of the canoe), towards the end where the child started. In order to maintain the center of mass of the system at rest, the canoe must move 2.5 m in the opposite direction.

Therefore, the canoe moves a total distance of 2.5 m + 0.5 m (the initial distance between the child and the end of the canoe) = 3.0 m in the water.

Hence, the correct choice is C) 3.0 m.

A 30-Kg Child Stands at One End of a Floating