Car B is 30 miles directly east of Car A and begins moving west at 90 mph. At the same moment car A begins moving north at 60 mph. What will be the minimum distance between the cars and at what time t does the minimum distance occur ?

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anonymous · Answer

|dw:1346212349272:dw|Lets consider the scenario after time t hours, car A would have moved due North by 60t miles to A' and car B would have moved due west by 90t miles to position B'|dw:1346212548852:dw| From Pythagoras theorem, you can say that $$AB'^2+AA'^2 = A'B'^2$$ here A'B' = d, we have to minimize d by using calculus; STEP I) differentiate d with respect to t, STEP II) put it equal to zero and solve for t, STEP III) Differentiate the derivative of d again and plug in the value obtained in step (ii) if the result is positive then you have the value of that would give you the minimum value of d. <This is called the double derivative test>