A motor-boat starts from a jetty O, travels upstream against the river flow for 12km at a constant speed of 6kmh−1, immediately turns around, and then travels downstream for 16km at 10kmh−1 to reach a picnic spot P. The river bank may be considered perfectly straight.
(a) Calculate the total distance covered by the motor-boat from O to P.
(b) Determine the displacement of the boat relative to the jetty when it reaches P, stating its magnitude and direction.
(c) Find the average speed for the entire journey from O to P.
(d) Find the magnitude of the average velocity for the same journey.