Chapter 5, Problem 7TS

To determine

The speed of the smaller fish before lunch.

Answer to Problem 7TS

The speed of the smaller fish is $5\text{m}/\text{s}$ before lunch.

Explanation of Solution

Given Info: The mass of the larger fish is $5\text{kg}$ , mass of the smaller fish is $1\text{kg}$ and speed of the larger fish before lunch is $1\text{m}/\text{s}$.

No external force is acting on both the fishes, so the momentum of both fishes will remains conserved.

Write the expression to calculate the speed of smaller fish before lunch.

$\begin{array}{c}M\cdot v=m\cdot u\\ u=\frac{M\cdot v}{m}\end{array}$

Here,

$M$ is the mass of the larger fish

$m$ is the mass of the smaller fish

$v$ is the speed of the larger fish

$u$ is the speed of the smaller fish before lunch

Substitute $5\text{kg}$ for $M$, $1\text{kg}$ for $m$ and $1\text{m}/\text{s}$ for $v$ in the above expression to find $u$.

$\begin{array}{c}u=\frac{\left(5\text{kg}\right)\left(1\text{m}/\text{s}\right)}{1\text{kg}}\\ =5\text{m}/\text{s}\end{array}$

Conclusion:

Therefore, the speed of the smaller fish is $5\text{m}/\text{s}$ before lunch.