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 clockwise from north) must she aim her canoe? How long will it take her to go directly across the river? Justify and explain your reasoning.

Answer 1

1. tanAr = -6/-2 = 3.0,
Ar = 71.6 Deg = Reference angle.
A = 180 + Ar = 180 + 71.6 = 251.6 Deg.

Da = 180 - 71.6 = 108.4 Deg.,CCW =
Direction she should aim her canoe.

2. d = V*t,
t = d/V = (2000/5280) / 2 = 0.1894 h =
11.4 min.

Answer 2

The only problem here is that when drawing your reference triangle, the westward speed was 2 and the downstream speed was 6, so you could take the tangent.

When rowing upstream, the 2 mph speed is along the hypotenuse, She can't row the required 2√10 = 6.32 mph needed to end up with a westward speed of 2 mph.

Answer 3

the x = arctan 2/6 = 18.43
so, the direction(measured clockwise) must be 18.43+ 180= 198.4 degrees.