A straight river flows at a speed of 20km/h. A boater starts at the south shore and heads in ths direction of 70degrees from the shore. The boat has a speed of 20km/h in still water. Find the true speed and direction of the boat.

Answer 1

Let the river flow in the +x direction.
Across the river is then +y.

river velocity = (20,0)
boat velocity relative to the water
= (20cos70°,20sin70°) = (6.84,18.79)

resultant velocity relative to land
= (26.84,18.79)

speed: √(26.8^2+18.79^2) = 32.73
direction:
tanθ = y/x = 18.79/26.84 = .70
θ = 35°