A 74-kg fisherman in a 124-kg boat throws a package of mass m = 15 kg horizontally toward the right with a speed of vi = 4.4 m/s as in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown.
Momentum is conserved. See "Related QuestIons" below for the method of solution.
17.5
To find the velocity of the boat after the package is thrown, we can apply the principle of conservation of momentum.
1. Determine the initial momentum before the package is thrown:
Momentum of the fisherman and boat = (mass of fisherman + mass of boat) × velocity of fisherman and boat
Momentum of fisherman and boat before = (74 kg + 124 kg) × 0 m/s (since the boat is at rest)
2. Determine the momentum of the package:
Momentum of package = mass of package × velocity of package
Momentum of package = 15 kg × 4.4 m/s
3. Apply the principle of conservation of momentum:
Total momentum before = Total momentum after
(74 kg + 124 kg) × 0 m/s + 15 kg × 4.4 m/s = (74 kg + 124 kg + 15 kg) × velocity of boat
4. Solve for the velocity of the boat:
(74 kg + 124 kg + 15 kg) × velocity of boat = 0 kg m/s + 66 kg m/s
(213 kg) × velocity of boat = 66 kg m/s
velocity of boat = 66 kg m/s / 213 kg
velocity of boat ≈ 0.3101 m/s
Therefore, the velocity of the boat after the package is thrown is approximately 0.3101 m/s to the right.