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Question

Two ships A and B are 10 km apart on a line running south to north. Ship A farther north is streaming west at 20 kmhr−1 and ship B is streaming north at 20 kmhr−1. How long do they take to reach distance of closest approach?

A
10 minute
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B
15 minute
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C
20 minute
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D
25 minute
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Solution

The correct option is B 15 minute
Ships A and B are moving with same speed 20 kmhr1 in the directions shown in figure. It is a two dimensional, two body problem with zero acceleration. Let us find vBA.


Here, vBA=(20)2+(20)2=202 kmhr1
i.e., vBA is 202 kmhr1 at an angle of 45 from east towards north. Thus, the given problem can be simplified as:
A is at rest and B is moving with vBA in the direction shown in figure.


therefore, the minimum distance between the two is
smin=AC=ABsin45=10(12) km=52 km
and the desired time is
t=BCvBA=52202 {BC=AC=52 km}t=14 hr=15 minutes

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