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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
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B
5h
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C
52h
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D
102h
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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

$$t=\dfrac{PQ}{V_{AB}}=\dfrac{50\sqrt2}{10\sqrt 2}=5\,h$$

1474444_1433877_ans_7e9aabc38a5a4189a0f05bdb0da0bc90.png

Physics

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