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?

Question

Physics

Paxton Schneider

18 March, 07:02

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?

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Answers (1)

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Walker Conway · 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.