Question

A canoe is designed to have very little drag when it moves along its length. Riley, mass 62 kg, sits in a 21 kg canoe in the middle of a lake. She dives into the water off the front of the canoe, along the axis of the canoe. She dives forward at 1.7 m/s relative to the boat.

1) Just after her leap, how fast is she moving relative to the water?
2) Just after her leap, how fast is the canoe moving relative to the water?

Answer 1

Just after her leap, Riley's velocity relative to the water would be 1.7 m/s. The canoe is at rest relative to the water just after Riley's leap.

Step-by-step explanation:

To answer the first question, we need to apply the principle of conservation of momentum. Just after her leap, Riley's mass and velocity would be transferred to the water, since momentum is conserved. The mass of the water displaced by Riley's leap is equal to 62 kg (Riley's mass). So, the velocity of Riley relative to the water is equal to her velocity relative to the boat, which is 1.7 m/s.

For the second question, we can use the same principle of conservation of momentum. The initial momentum of the canoe and Riley combined is zero, since they were at rest. After Riley's leap, the canoe gains momentum in the opposite direction to compensate for Riley's leap. Since Riley's mass is much smaller than the total mass of the canoe, the velocity of the canoe relative to the water would be very small compared to Riley's velocity. Therefore, the canoe is practically at rest relative to the water just after Riley's leap.