Question

a 5-kg fish swimming at 1 m/s swallows an absent minded 1-kg fish at rest. What is the speed of the large fish immediately afyer lunch? What would its speed be if the small dish were swimming toward it at 4 m/s?

Answer 1

Answer:

In first case speed of fish will be $\frac{5}{6}$ m/s.

In the second case the speed of fish $\frac{1}{6}$ m/s

Explanation:

Given data :-

Mass of bigger fish ( m₁ ) = 5 kg.

Mass of small fish ( m₂ ) = 1 kg.

Speed of large fish ( v₁ ) = 1 m/s

Mass of bigger fish after eating smaller one = 5 + 1 = 6 kg.

Case - 1

Momentum of bigger fish before eating the smaller fish = m₁* v₁ = 5 * 1 = 5 kg.m/s

Momentum of bigger fish after eating the larger fish = ( m₁ + m₂)*v

v = speed of bigger fish immediately after lunch.

Using the conservation of momentum.

m₁* v₁ = ( m₁ + m₂)*v

5 = 6 * v

v = $\frac{5}{6}$  m/s.

Case -2

Speed of small fish = 4 m/s

Momentum of bigger fish before lunch = 5 kg.m/s

Momentum of smaller fish before lunch = 4*1 = 4 kg.m/s

Net momentum before lunch = 5 - 4 = 1 kg.m/s

Momentum of bigger fish after eating the larger fish = 6 * V

Using the conservation of momentum.

1 = 6 * V

V = $\frac{1}{6}$ m/s.

Answer 2

In the first case when the speed of the fish will be 5/6 m/s.

In the second case when the speed of fish is = 1/6 m/s

Calculation of Speed Large Fish

Given data as per question:-

The Mass of bigger fish ( m₁) is = 5 kg.

Then, the Mass of small fish ( m₂) is = 1 kg.

After that, Speed of large fish ( v₁ ) = 1 m/s

Mass of bigger fish after eating smaller one = 5 + 1 = 6 kg.

Case - 1 When the Momentum of bigger fish before eating the smaller fish = m₁* v₁ = 5 * 1 = 5 kg.m/s

Then, the Momentum of bigger fish after eating the larger fish = (m₁ + m₂)*v

Now, v is = speed of bigger fish immediately after lunch.

Now we are using the conservation of momentum.

Then, m₁* v₁ = ( m₁ + m₂)*v

5 = 6 * v

Therefore, v = 5/6 m/s.

Case -2 When the Speed of small fish = 4 m/s

Then, the Momentum of bigger fish before lunch is = 5 kg.m/s

Now, the Momentum of smaller fish before lunch = 4*1 = 4 kg.m/s

Then, Net momentum before lunch = 5 - 4 = 1 kg.m/s

After that, the Momentum of bigger fish after eating the larger fish = 6 * V

Now, Using the conservation of momentum.

1 = 6 * V

Thus, V = 1/6 m/s.

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