an 85kg fisherman jumps from a dock into a 135kg rowboat at rest on the west side of the dock, if the velocity of the fisherman is 4.3m/s to the west as he lives the dock, what is the final velocity of the fisherman and the boat?
Ur dad.
The fisherman is jumping into the boat so their masses become combined as they are one "object".
momentum of the system is conserved, so (ignoring the very real resistance of the water)
4.3*85 = (85+135)v
v = 1.66 m/s
I approve
To find the final velocity of the fisherman and the boat, we can apply the law of conservation of momentum. According to this law, the total momentum before the jump should be equal to the total momentum after the jump.
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Before the jump, we have two objects with their own momentum:
Fisherman's initial momentum = mass of the fisherman × initial velocity of the fisherman
Rowboat's initial momentum = mass of the rowboat × initial velocity of the rowboat
Since the rowboat is at rest initially, its initial velocity is 0 (zero). Hence, its initial momentum would also be zero.
Therefore, the momentum before the jump is simply the momentum of the fisherman:
Initial momentum = mass of the fisherman × initial velocity of the fisherman
To calculate the final velocity, we'll use the conservation of momentum:
(total initial momentum) = (total final momentum)
The total initial momentum includes only the momentum of the fisherman. The total final momentum includes the momentum of both the fisherman and the rowboat.
(total initial momentum) = (total final momentum)
mass of the fisherman × initial velocity of the fisherman = (mass of the fisherman + mass of the rowboat) × final velocity
Plugging in the given values:
mass of the fisherman = 85 kg
initial velocity of the fisherman = -4.3 m/s
mass of the rowboat = 135 kg
final velocity (to be calculated) = ?
85 kg × (-4.3 m/s) = (85 kg + 135 kg) × final velocity
Now we can solve for the final velocity:
-365.5 kg·m/s = 220 kg × final velocity
final velocity = (-365.5 kg·m/s) / 220 kg
final velocity ≈ -1.661 m/s
Therefore, the final velocity of both the fisherman and the rowboat is approximately -1.661 m/s to the west. (The negative sign indicates that the direction is west.)