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Distance of closest approach of two ships problem

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Two ships are 10 km apart on a line running south to north. The one farther north is steaming west at 20 km/h. The other is steaming north at 20 km/h. What is their distance of closest approach? How long do they take to reach it?

Asked Gayathri

Solution and Answer:

The main hindrance to solving problem is that students fail to visualize the situation.

Let’s represent the condition using a diagram.

Let the first ship steaming north be named A and the other B. The relative velocity of A with respect to B is 20 √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 sin 45° = 10/√2 = 7.07 m

Time taken to reach the distance of closest approach = distance of closest approach / relative speed

= (10/√2)/(20 √2)

= 0.25 h

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