Question

A river is 2000 ft wide and flowing at 6 mph from north to south. A woman in a canoe starts on the eastern shore and heads west at her normal paddling speed of 2 mph. In what direction (measured from North) will she actually be traveling. How far downstream from a point directly across the river will she land?

Answer 1

she is traveling on an angle west of south
... the tangent of the angle is ... 2/6

the river is flowing 3 times as fast as the woman paddles
... she will end up three times the width of the river , downstream

Answer 2

All angles are measured CW from +y-axis.
a. Vr = 2mi/h[270] + 6mi/h[180o],
Vr = (2*sin270+6*sin180) + (2*cos270+6*cos180)I,
Vr = (-2+0) + (0-6)I = -2 - 6i = 6.32[18.4o] W of S. = 6.32mi/h[198.4o] CW.
Direction = 198.4 degrees CW.

b. Tan18.4 = 2000/Y,
Y = 6,012 Ft. downstream.