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 law of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event in the absence of external forces.
The momentum of an object is given by the product of its mass and velocity. Therefore, the initial momentum of the fisherman is given by:
Initial momentum of fisherman = mass of fisherman × velocity of fisherman
= 86 kg × (-3.4 m/s) (since the velocity is stated to be to the West)
= -292.4 kg·m/s
The initial momentum of the rowboat is given by:
Initial momentum of rowboat = mass of rowboat × velocity of rowboat
= 121 kg × 0 m/s (since the rowboat is at rest initially)
= 0 kg·m/s
The total momentum before the fisherman jumps is the sum of the individual momenta of the fisherman and the rowboat:
Total initial momentum = Initial momentum of fisherman + Initial momentum of rowboat
= -292.4 kg·m/s + 0 kg·m/s
= -292.4 kg·m/s
According to the law of conservation of momentum, the total momentum after the fisherman jumps must also be -292.4 kg·m/s. Let's assume the final velocity of the fisherman and the rowboat is v.
The final momentum of the fisherman is:
Final momentum of fisherman = mass of fisherman × final velocity of fisherman
= 86 kg × v
The final momentum of the rowboat is:
Final momentum of rowboat = mass of rowboat × final velocity of rowboat
= 121 kg × v
Since the total momentum after the fisherman jumps is the sum of the individual momenta, we can write:
Total final momentum = Final momentum of fisherman + Final momentum of rowboat
-292.4 kg·m/s = 86 kg × v + 121 kg × v
Simplifying the equation:
-292.4 kg·m/s = (86 kg + 121 kg) × v
-292.4 kg·m/s = 207 kg × v
Dividing both sides of the equation by 207 kg:
v = -292.4 kg·m/s / 207 kg
v ≈ -1.41 m/s
Therefore, the final velocity of the fisherman and the rowboat is approximately -1.41 m/s to the West.