A canoe has a velocity of 0.39 southeast relative to the earth. The canoe is on a river that is flowing 0.59 east relative to the earth.

Question

Find the magnitude of the velocity of the canoe relative to the river.
Find the direction of the velocity of the canoe relative to the river

Answer 1

Do a vector subtraction of the river water velocity from the velocity of the canoe relative to earth.

Velocity relative to Earth
= 0.27577 i - 0.2577 j
(i is east unit vector; j is north unit vector)
Velocity of river relative to Earth
= 0.59 i
Velocity of canoe relative to water:
= -0.31423 i -0.2577 j
magnitude of above = 0.4064

You forgot to include the dimension of the velocity number.