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.