A 5-kg fish swimming at a velocity of 1 m/s swallows an absent-minded 1-kg fish swimming towards it 4 m/s. Wha tis the speed of the larger fish after lunch?

Question

Adrian Ayala · Accepted Answer

I found #0.17m/s#

We can use conservation of momentum in the #x# direction:

Emily Abbate · Answer

undefined To find the speed of the larger fish after lunch, we can use the principle of conservation of momentum.

The momentum before lunch is equal to the momentum after lunch.

The momentum of the larger fish before lunch is given by its mass (5 kg) multiplied by its velocity (1 m/s), which equals 5 kg*m/s.

The momentum of the smaller fish before lunch is given by its mass (1 kg) multiplied by its velocity (4 m/s), which equals 4 kg*m/s.

The total momentum before lunch is the sum of these individual momentums, which equals 5 kg*m/s + 4 kg*m/s = 9 kg*m/s.

Since momentum is conserved, the total momentum after lunch must also equal 9 kg*m/s.

Now, the larger fish has consumed the smaller fish, so their masses have combined.

The total mass after lunch is 5 kg (mass of the larger fish) + 1 kg (mass of the smaller fish) = 6 kg.

To find the velocity of the larger fish after lunch, we divide the total momentum (9 kg*m/s) by the total mass (6 kg).

So, the velocity of the larger fish after lunch is 9 kg*m/s divided by 6 kg, which equals 1.5 m/s.

Therefore, the speed of the larger fish after lunch is 1.5 m/s.