Question

A river flows due south at 1.4 mi/h. In what direction should the swimmer head, at a velocity of 3 mi/h, in order to arrive at a landing point due east of his starting point? (Round your answer to one decimal place.)

Answer 1

Solution:

It is that a river is flowing in the south direction with a speed of $v_r$1.4 mi/h.

A swimmer wishes to cross the river in a horizontal direction so that he lands at a point which is due east of his starting point.

The speed of the swimmer is $v_s$ = 3 mi/h

Therefore he has to swim in such a direction that his resultant is in the direction east to his starting point.

Let this angle be θ.

Therefore, from the figure,

$\sin \theta = \frac{v_r}{v_s}$

$\sin \theta = \frac{1.4}{3}$

$\theta = \sin^{-1}(0.46)$

  $=27.4^\circ$

Therefore, the swimmer has to swim in the northeast direction making an angle of (90+27.4) = 117.4° with the direction of flow of river (i.e. south).