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Suppose at one point along the Nile River a ferryboat must travel straight across a 1.40-mile stretch from west to east. At this location, the river flows from south to north with a speed of 2.35 m/s. The ferryboat has a motor that can move the boat forward at a constant speed of 21.8 mph in still water. In what direction should the ferry captain direct the boat so as to travel directly across the river?

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sqdancefan

Answer:

  about 14° south of east

Step-by-step explanation:

The river speed is about ...

  (2.35 m/s)×(1 mi/(1609.344 m))×(3600 s)/(1 h) ≈ 5.2568 mi/h

The angle of interest is such that its sine is the ratio of river speed to boat speed:

  sin(α) = (5.2568 mi/h)/(21.8 mi/h) = 0.241138

  α = arcsin(0.241138) = 13.9537°

Since the river is flowing north, the boat should be directed south of its intended course by this angle.

The boat should be directed 14° south of east.

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