Question

# A ship A is moving Westwards with a speed of 10 km $$h^{-1}$$ and a ship B 100 km South of A is moving northwards with a speed of 10 km $$h^{-1}$$. The time after which the distance between them becomes shortest is

A
0h
B
5h
C
52h
D
102h

Solution

## The correct option is B $$5 h$$It is clear from the diagram that the shortest distance between the ship $$A$$ and $$B$$ is $$PQ$$.Here, $$Sin\,45^0=\dfrac{PQ}{OQ}$$$$\implies PQ=100\times \dfrac{1}{\sqrt 2}=50\sqrt 2\,m$$Also,$$V_{AB}=\sqrt{V_A^2+V_B^2}=\sqrt{10^2+10^2}=10\sqrt 2\,km/h$$So, the time taken to reach shortest path is$$t=\dfrac{PQ}{V_{AB}}=\dfrac{50\sqrt2}{10\sqrt 2}=5\,h$$Physics

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