Question

Two people, one of mass 87 kg and the other of mass 55 kg, sit in a rowboat of mass 67 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat 3.5 m apart from each other, now exchange seats. What is the final velocity of the boat after the exchange of seats?

A) 0 m/s
B) 0.15 m/s
C) 0.30 m/s
D) 0.45 m/s

Answer 1

The final velocity of the boat after the exchange of seats is 0 m/s.

Step-by-step explanation:

To find the final velocity of the boat after the exchange of seats, we can use the principle of conservation of momentum. The initial momentum of the system, which includes the boat and the two people, is zero since the boat is initially at rest. After the exchange of seats, the total momentum of the system is still zero.

The momentum of the boat is given by the equation:

Mass of the boat * final velocity of the boat = (-Mass of Person 1 * initial velocity of Person 1) + (-Mass of Person 2 * initial velocity of Person 2)

Plugging in the values, we get:

(67 kg) * (final velocity of the boat) = (-87 kg) * (0 m/s) + (-55 kg) * (0 m/s)

Simplifying the equation, we find that the final velocity of the boat after the exchange of seats is 0 m/s.