A boat can move through still water with a velocity of 4m s−1 due East. The river, however, flows steadily southwards with a speed of 3m s−1.
a. (i) Determine the components of the boat’s velocity relative to the ground.
b. (ii) Hence obtain the magnitude of the boat’s velocity relative to the ground.
c. (iii) Calculate the angle between this velocity and the East direction. State clearly the quadrant in which the resultant velocity lies.
d. (iv) If the river is 200m wide, find the time taken by the boat to reach the opposite bank.