Answer: (A) 26kgm/s (B) 2.6m/s
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 [tex]p[/tex] does.
Thus: [tex]p=m.V[/tex] (1)
Where [tex]m[/tex] is the mass and [tex]V[/tex] the velocity.
[tex]p_{i}=p_{f}[/tex] (2)
Where [tex]p_{i}[/tex] is the initial momentum and [tex]p_{f}[/tex] the final momentum.
(A) Momentum of the two fish system after the smaller fish has been swallowed
[tex]p_{i}=m_{i1}V_{i1}+m_{i2}V_{i2}[/tex] (3)
Where [tex]m_{i}=8kg[/tex] is the initial mass (mass of the big fish) and [tex]V_{i}=3m/s[/tex] is the initial velocity of the big fish, [tex]m_{i2}=2kg[/tex] is the initial mass of the small fish and [tex]V_{i2}=1m/s[/tex] is the initial velocity of the small fish.
[tex]p_{i}=(8kg)(3m/s)+(2kg)(1m/s)=26kg.m/s[/tex] (4)
By the conservation of linear momentum:
[tex]p_{i}=p_{f}=26kg.m/s[/tex] (5)
(B) Speed of the two fish system after the smaller fish has been swallowed
In this case we will focus on [tex]p_{f}[/tex] (after the "collision"):
[tex]p_{f}=(m_{i1}+m_{i2})V[/tex] (6)
Where [tex]V[/tex] is the velocity of the system of both fish.
Finding [tex]V[/tex]:
[tex]V=\frac{p_{f}}{m_{i1}+m_{i2}}[/tex] (7)
Solving (7) and remembering [tex]p_{i}=p_{f}[/tex]:
[tex]V=\frac{26kg.m/s}{8kg+2kg}[/tex] (8)
Finally:
[tex]V=2.6m/s[/tex]
