Question

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.)

Answer 1

Answer: (A) 26kgm/s (B) 2.6m/s

Step-by-step 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
`p` does.

Thus:
`p=m.V` (1)

Where
`m` is the mass and
`V` the velocity.

`p_(i)=p_(f)` (2)

Where
`p_(i)` is the initial momentum and
`p_(f)` the final momentum.

(A) Momentum of the two fish system after the smaller fish has been swallowed

`p_(i)=m_(i1)V_(i1)+m_(i2)V_(i2)` (3)

Where
`m_(i)=8kg` is the initial mass (mass of the big fish) and
`V_(i)=3m/s` is the initial velocity of the big fish,
`m_(i2)=2kg` is the initial mass of the small fish and
`V_(i2)=1m/s` is the initial velocity of the small fish.

`p_(i)=(8kg)(3m/s)+(2kg)(1m/s)=26kg.m/s` (4)

By the conservation of linear momentum:

`p_(i)=p_(f)=26kg.m/s` (5)

(B) Speed of the two fish system after the smaller fish has been swallowed

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

`p_(f)=(m_(i1)+m_(i2))V` (6)

Where
`V` is the velocity of the system of both fish.

Finding
`V`:

`V=(p_(f))/(m_(i1)+m_(i2))` (7)

Solving (7) and remembering
`p_(i)=p_(f)`:

`V=(26kg.m/s)/(8kg+2kg)` (8)

Finally:

`V=2.6m/s`