Question

Is the same time necessary for a cutter to travel a distance of 1 km upstream and back on a river (current velocity is equal to 2 km/hr) as on a lake (in still water) if the velocity of the cutter relative to the water is, in both cases, 8 km/hr? Solve the problem analytically and graphically.

Answer 1

Answer: The time of travel on the river is 1.07 times that on the lake. 

Explanation:

The time of travel upstream on the river is t₁ = S/(v₂ —v₁), where S = 1km, v₁ = 2km/hr, v₂ = 8km/hr. The time of travel downstream is t₂ = S/(v₂ + v₁). 

The total time of travel on the river (there and back) is 

t = t₁ + t₂ = 2Sv₂/(v²₂ — v²₁). 

The time of travel there and back on the lake is t₃ = 2S/v₂ . The ratio of the two times is

t/t₃ = v²₂/(v²₂ - v²₁) = 1.07.

Figure represents a plot of the motion: I is the motion in still water, II is the motion in the river; t₃ and t are the corresponding times in each case.