A 3 kg fish swimming 5 m/s swallows an absent minded 1 kg fish at rest?

[Nathan M]

What is the speed of the large fish immediately after lunch?
What would its speed be if the small fish were swimming towards it at 4 m/s?

 

[NZKhan]

Momentum
(m1 x V1) + (m2 x V2) = V3(m1 + m2)

(3 x 5) + (1 x 0) = V3(3 +1)
15 = 4V3
V3 = 15/4 = 3.75 m/s

(m1 x V1) + (m2 xV2) = V3(m1 + m2)
(3 x 5) + (1 x -4) = V3(3 + 1)
15 - 4 = 4V3
V3 = 11/4 = 2.75 m/s

 

[wjllope]

conserve momentum

initial: 3kg*5m/s + 0
final: 4kg*V
V = (15/4) m/s = 3.75 m/s

again, conserve momentum

initial: 3kg*5m/s + 1kg(-4m/s)
final: 4kg*V
V = (11/4) m/s = 2.75 m/s