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Question

Two ships are 10√2 km apart on a line joining south to north. The one further north is moving west with a speed of 25km/h while the other towards north with a speed of 25 km/h . What is their distance of closest approach and how long do they take to reach it?

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Solution

Let the first ship steaming north be named A and the other B. The relative velocity of A with respect to B is 25 √2 south west. If we extend the line along the 45° south west from the initial position of A, the distance of closest approach is the perpendicular drawn from B to this line. So, the distance of closest appraoch = 10√2 sin 45° = 10√2/√2 = 10 m Time taken to reach the distance of closest approach = distance of closest approach / relative speed = (10)/(25√2) = 0.56 h

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