PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A boat can move through still water with speed 5ms−1. It is to cross a straight river 200m wide in the shortest possible time. The water in the river flows eastward with speed 3ms−1.
Treat the boat’s velocity relative to water as a vector of fixed magnitude but variable direction. The required motion is such that the boat reaches a point directly north of its starting position on the opposite bank (that is, the resultant displacement has no eastward drift).
Answer the following:
(i) Let the boat’s heading make an angle ϕ west of north. Write component equations for the ground-velocity of the boat in terms of ϕ.
(ii) Determine the angle ϕ that satisfies the condition of zero eastward drift.
(iii) Calculate the time taken for the boat to cross the river under this optimum heading.
(iv) Find the speed of the boat with respect to the ground for this motion.