A 86kg fisherman jumps from a dock into a 121kg rowboat at rest on the West side of the dock.
If the velocity of the fisherman is 3.4m/s to the West as he leaves the dock, what is the final velocity of the fisherman and the rowboat?
Answer in units of m/s
To solve this problem, we can use the principles of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as there are no external forces acting on the system.
Before the fisherman jumps into the rowboat, both the fisherman and the rowboat are at rest, so their initial velocity (v_i) is 0 m/s.
The momentum (p) of an object is calculated as the product of its mass (m) and its velocity (v): p = m * v.
Using this formula, the initial momentum of the fisherman can be calculated as:
Initial momentum of the fisherman = mass of the fisherman (86 kg) * velocity of the fisherman (0 m/s) = 0 kg * m/s.
The initial momentum of the rowboat can be calculated as:
Initial momentum of the rowboat = mass of the rowboat (121 kg) * velocity of the rowboat (0 m/s) = 0 kg * m/s.
Therefore, the total initial momentum of the system (fisherman + rowboat) is 0 kg * m/s.
After the fisherman jumps into the rowboat, the total mass of the system is the sum of the mass of the fisherman and the mass of the rowboat, which is 86 kg + 121 kg = 207 kg.
Let's assume the final velocity of both the fisherman and the rowboat after the jump is V m/s.
The total final momentum of the system is calculated as:
Total final momentum = total mass of the system * final velocity of the system = 207 kg * V.
According to the conservation of momentum principle, the total initial momentum of the system is equal to the total final momentum of the system:
0 kg * m/s = 207 kg * V.
To find the final velocity (V), we can rearrange the equation:
V = (0 kg * m/s) / (207 kg) = 0 m/s.
Therefore, the final velocity of both the fisherman and the rowboat is 0 m/s to the West.