A river is 200m wide and flows due east with a uniform speed of 1.5m s−1 relative to the ground. A small motorboat can move through still water at a speed of 3.0m s−1. The pilot aims the boat so that its bow points 30∘ west of north while crossing.
(a) Determine the boat’s velocity (magnitude and direction) relative to the ground while it is aimed 30∘ west of north.
(b) Calculate the time required for the boat to reach the opposite bank.
(c) Find how far downstream (east or west of the point directly opposite the launch point) the boat lands on the far shore.