Two people, one of mass 70 and the other of mass 65 , sit in a rowboat of mass 78 . With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 3.5 apart from each other, now exchange seats.
To determine the final velocity and direction of the rowboat after the two people exchange seats, we need to apply the principle of conservation of momentum.
1. Find the initial momentum:
The total initial momentum is equal to the sum of the momenta of the three objects (two people and the rowboat) before the seat exchange. Momentum is calculated by multiplying mass and velocity.
Initial momentum = (70 kg * 0 m/s) + (65 kg * 0 m/s) + (78 kg * 0 m/s) = 0 kg·m/s
2. Find the final momentum:
The total final momentum is equal to the sum of the momenta of the three objects after the seat exchange.
Since no external forces are acting on the system (neglecting friction and other factors), the total momentum before the seat exchange is equal to the total momentum after the seat exchange.
Therefore, the final momentum is also 0 kg·m/s.
3. Determine the final velocity of the rowboat:
The final velocity of the rowboat can be calculated using the equation:
Total final momentum = (Mass of rowboat + Mass of person 1 + Mass of person 2) * Final velocity of rowboat
0 kg·m/s = (78 kg + 70 kg + 65 kg) * Final velocity of rowboat
0 kg·m/s = 213 kg * Final velocity of rowboat
Since the mass of the rowboat and the combined mass of the two people is positive, the final velocity of the rowboat must be zero. This means the rowboat will remain at rest after the seat exchange.
Therefore, the final velocity and direction of the rowboat is 0 m/s (at rest).
Numbers without units are useless in physics.
You should know that by now.