A ship A is moving Westwards with a speed of 10 k m h - 1 and a ship B 100 km south of A , is moving…

1. $0\mathrm{ }\mathrm{h}$
2. $5\mathrm{ }\mathrm{h}$
3. $5\sqrt{2}\mathrm{ }\mathrm{h}$
4. $10\sqrt{2}\mathrm{ }\mathrm{h}$

Solution

Relative velocity of ship B is,
$\left|{\overrightarrow{\mathrm{V}}}_{\mathrm{B}\mathrm{A}}\right|=\sqrt{{10}^{2\mathrm{ }}+{10}^2}=10\sqrt{2}\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{p}\mathrm{h}$
Let shortest distance between ship A & B is AO,
Distance $\mathrm{O}\mathrm{B}=100\cos {45}^{\mathrm{o}}=50\sqrt{2}\mathrm{ }\mathrm{k}\mathrm{m}$
Hence time taken to reach the shortest distance,
$\mathrm{t}=\frac{50\sqrt{2}}{10\sqrt{2}}=5\mathrm{h}\mathrm{r}\mathrm{s}$

Asked in: NEET 2015 (Phase 1)

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