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The Closest Approach between Two Boats

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Mike, who is standing on the deck of a yacht that is traveling due west at 6km/h, sees a sailboat sailing southwest at 4km/h, 3 km northwest of the yacht. How close to each other do these boats get?

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Solution Summary

Neat and Step-by-step solution is provided. Graph included showing the point of minimum distance.

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Assume that Mike's yacht is at the origin. After t hrs, its position is given by P(-6t, 0)
The sailboat is at the point (-3 cos 45º, 3 sin 45º) = (-3√2/2, 3√2/2). After t hrs, its ...

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