31. a big 8 kg fish swimming at 3 m/s opens its mouth and swallows a small 2 kg fish swimming
away from it at 1 m/s. presume water resistance is negligible. show your calculations.
(a) what is the momentum of the two fish system after the smaller fish has been
swallowed?
(b) what is the speed of the two fish system after the smaller fish has been swallowed?
(hint: first figure the mass of the two fish system.)

Explanation:

This problem is a good example of an inelastic collision, in which the elements that collide remain together after the collision, and althogh the kinetic energy is not conserved, the linear momentum does.

Thus:  (1)

Where is the mass and the velocity.

 (2)

Where is the initial momentum and the final momentum.

(3)

Where is the initial mass (mass of the big fish) and is the initial velocity of the big fish, is the initial mass of the small fish and is the initial velocity of the small fish.

(4)

By the conservation of linear momentum:

(5)

In this case we will focus on (after the "collision"):

(6)

Where is the velocity of the system of both fish.

Finding :

(7)

Solving (7) and remembering :

(8)

Finally:

heat the gas and measure the pressure