To solve this problem, we need to use the principle of conservation of momentum. The momentum before the exchange of seats is equal to the momentum after the exchange.
Initially, the boat is at rest, so the total momentum is zero.
The momentum of each person can be calculated using the formula: momentum = mass × velocity.
Let's assume the person with a mass of 85 kg moves to the other end of the boat. To calculate their final velocity, we can use the equation: momentum = mass × velocity. Since the boat is at rest initially, and there is no external force acting on it, the change in momentum of the person will be equal in magnitude to the change in momentum of the boat.
The person's initial momentum = mass × velocity = 85 kg × 0 m/s = 0 kg•m/s (since the person is initially at rest).
The person's final momentum = mass × final velocity.
To find the final velocity, we can rearrange the equation for momentum:
final velocity = final momentum / mass.
The final momentum for the person is 0 kg•m/s since they started and ended at rest.
By substituting the known values into the equation, we find:
final velocity = 0 kg•m/s / 85 kg = 0 m/s.
Therefore, the person's final velocity is 0 m/s, indicating that they didn't move.
Since the person with a mass of 50 kg exchanged seats, the same principle applies. The final momentum for that person is also 0 kg•m/s, and their final velocity is 0 m/s.
So, we can conclude that the final momentum of the boat is 0 kg•m/s as well.
Now, let's determine the initial momentum of the boat. It is the combined momentum of the two people sitting at opposite ends.
Using the formula momentum = mass × velocity:
Initial momentum of the 85 kg person = 85 kg × 0 m/s = 0 kg•m/s.
Initial momentum of the 50 kg person = 50 kg × 0 m/s = 0 kg•m/s.
So, the initial momentum of the boat is 0 kg•m/s as well.
According to the principle of conservation of momentum (initial momentum = final momentum), the boat, with a mass of 90 kg, will have no net change in momentum before and after the seat exchange. Therefore, the boat will remain at rest, and it will not move.