Suppose a fish swimming a distance of L ft at a speed of v fit/sec relative to the water against a current flowing at the rate of u ft/sec (u<v) expends a total energy given by

Question

E(v)= (aLv^3)/(v-u)
Where E is measured in foot-pounds and a is a constant.

a) Evaluate the limit of E(v) as v-->u+ and interpret your result
b) Evaluate the limit of E(v) as v-->infinity and interpret your result

Answer 1

a) as v -> u the Energy required becomes infinite because the fish does not move and requires infinite time to go a distance L.

b) as v--> infinity, the energy required is proportional to v^2 (which is true for the fluid drag force), as the stream velocity becomes negligible compared to v.

Energy = force x distance.

Answer 2

Could you please show me the math behind answer a? How did you calculate the limit to get infinity?