A river 500m wide flows steadily with a current of 3ms−1 from west to east. A boat can be rowed at 4ms−1 relative to still water and is aimed due north.
(i) Determine the magnitude and direction of the boat’s velocity relative to the ground.
(ii) Calculate the time taken by the boat to reach the opposite bank.
(iii) Find the distance downstream from the point directly opposite the starting point at which the boat lands.