A 5-kg fish swimming at a speed of 1 m/s swallows an absent-minded 1-kg fish at rest. The speed of the larger fish after this lunch is

Question

Quizplus · Accepted Answer

The conservation of momentum principle applies here. Before the larger fish swallows the smaller one, the total momentum of the system is the momentum of the larger fish since the smaller fish is at rest. The momentum of the larger fish is its mass times its velocity, which is $5 \, \text{kg} \times 1 \, \text{m/s} = 5 \, \text{kg} \cdot \text{m/s}$. After swallowing the smaller fish, the total mass of the system is $5 \, \text{kg} + 1 \, \text{kg} = 6 \, \text{kg}$. To conserve momentum, the total momentum after the event must equal the total momentum before the event. Thus, $5 \, \text{kg} \cdot \text{m/s} = 6 \, \text{kg} \times v$, where $v$ is the velocity of the combined mass after the event. Solving for $v$, we find $v = 5/6 \, \text{m/s}$.

A 5-Kg Fish Swimming at a Speed of 1 M/s