Question

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?

Answer 1

See the diagram,it explains what the situation is going to be for achieving the purpose,

`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`