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21 June, 03:08

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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  1. 21 June, 03:10
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    - - 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.
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