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Ship A is sailing toward the west at 10 km h⁻¹. Ship B is located 100 km due south of A and is moving northward at 10 km h⁻¹. After how much time will the separation between the two ships be minimum?

1. 5 h
2. 5√2 h
3. 10√2 h
4. 0 h

Correct answer: 5 h

Solution

Take A at origin moving west (-10,0) and B at (0,-100) moving north (0,10). Separation squared = (10t)^2 + (10t-100)^2; minimizing gives 200t + 200t - 2000 = 0, so t = 5 h.

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