Question: A boat moves relative to water with a velocity v and river is flowering with 2v. At what angle the b...

Question

A boat moves relative to water with a velocity v and river is flowering with 2v. At what angle the boat shall move with the stream to have minimum drift?

Answer 1

Solution

Let boat move at angle θ to the normal as shown in fig. then time to cross the river = l/v cos θ.

drift x = (2v – vsin θ) l/v cos θ for x to be minimum

dx/dθ = 0 = 1(2 secθ tan θ - sec²θ) or sin θ = 1/2

or θ = 30⁰ and φ = 90 + 30 = 12⁰