A boat must sail directly south across a river 200 m wide. This river flows west

Question

A boat must sail directly south across a river 200 m wide. This river flows west at 1.2 m s^-1. In still water the boat sails at a speed of 2.0 m s^-1. Sketch a labelled vector diagram showing the relationship between: the velocity of the boat relative to the water, the velocity of the current (i.e. the velocity of the water relative to the river bank), and the velocity of the boat relative to the river-bank. Hence (or otherwise) find the direction in which the boat should point (i.e. its heading). Calculate the time taken to cross the river

Explanation / Answer

Here, velocity of boat in still water = (1.2 i - 1.6 j) m/s

Thus, velocity of boat relative to river =   (1.2 i - 1.6 j) + (- 1.2 i)

                                                              =   - 1.6 j m/s

direction in which boat should point = tan-1(1.6/1.2)

                                                         = 53.13 degree South East

time taken to cross river = 200/1.6

                                        = 125 s

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