Multiple choice

A boat moves relative to water with a velocity half of the river flow velocity if the angle from the direction of flow with which boat must move relative to stream directly to minimize drift is $\dfrac{2\times \pi }{n}$, then n is:

  1. 1

  2. 0

  3. 4

  4. 3

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To minimize drift, the boat must head at an angle theta such that its velocity component perpendicular to the river flow cancels the river flow velocity. If v is boat speed and u is river speed, sin(theta) = v/u. Given v = u/2, sin(theta) = 1/2, so theta = 30 degrees or pi/6. The question asks for the angle from the direction of flow, which is 90 + 30 = 120 degrees or 2pi/3. Thus n=3.