Question

A boat is trying to head due west across a river at 20 m/s. If the river current pushes it off course by flowing 15 m/s due south, what would be the resultant velocity of the boat? If the river is 600 m wide how long does it take to get across? How far downstream will the boat land?

Answer 1

-- The boat's speed is  √(20² + 15²)

                               =  √(400 + 225)

                               =  √(625 m²/s²)  =  25 m/s .

-- Its direction is    tan⁻¹(15/20) = tan⁻¹(0.75) = about 36.9° south of west.

-- Its velocity  =  25 m/s heading 36.9° south of west .


-- Heading west at 20 m/s across the 600-m channel
it takes the boat
                                     (600 m) / (20 m/s)  =  30 seconds
to hit the opposite bank.

-- In that 30 seconds, the current will carry the boat

           (15 m/s) x (30 sec)  =  450 meters downstream, south.