A 125 kg flatbottomed boat is floating along at 5.0 m/s, headed east. Sally Sue, standing at one
end of the boat, starts to walk at 2.0 m/s, also to the east. If Sally’s mass is 65 kg, what is the
speed of the boat as she walks along?
To find the final speed of the boat as Sally walks along, we need to apply the principle of conservation of momentum.
The total momentum before Sally starts walking is equal to the total momentum after she starts walking.
Let's define the positive direction as eastward. The momentum of the boat before Sally starts walking is given by:
Momentum of boat before = mass of boat * velocity of boat
Momentum of boat before = 125 kg * 5.0 m/s = 625 kg·m/s
Sally starts walking with a velocity of 2.0 m/s in the same direction as the boat. The momentum of Sally after she starts walking is given by:
Momentum of Sally after = mass of Sally * velocity of Sally
Momentum of Sally after = 65 kg * 2.0 m/s = 130 kg·m/s
Since momentum is conserved, the total momentum after Sally starts walking is the sum of the momenta of the boat and Sally before she starts walking.
Total initial momentum = Total final momentum
(125 kg * 5.0 m/s) = (125 kg + 65 kg) * final velocity
625 kg·m/s = 190 kg * final velocity
Now we can solve for the final velocity of the boat:
final velocity = 625 kg·m/s / 190 kg
final velocity ≈ 3.289 m/s
So, the final speed of the boat as Sally walks along is approximately 3.289 m/s, still headed east.