A stream 50m wide is flowing at 15m/s. Isaac can swim at a speed of 20m/s in calm water. In what direction ( angle ) must Isaac set off if he must reach the opposite bank by the shortest route?

1 Answer
Mar 1, 2018

See the diagram,it explains what the situation is going to be for achieving the purpose,enter image source here

#AC# is the path which Issac would have gone,in absence of river flow,but river will push him by #CB# so,he will reach at point #B# on the opposite bank of the river.

So,let he starts swimmimg at an angle #theta# w.r.t the river bank,so his component of velocity,along the direction of river flow is #20 cos theta#,which is acting against the direction of river flow i.e #15 ms^-1#,so both must be equal,so that he just reaches point #B#,

So,we get, # 20 cos theta = 15#

or, #cos theta = 15/20 =3/4#

So,#theta=41.41^@#

So,he will move from #A# to #B# with velocity #20 sin 41.41=13.23 ms^-1#

So,time taken to reach #B# from #A# will be #50/13.23=3.78s#