A ship $\text{A}$ is moving Westwards with a speed of $10\mathrm{ }\mathrm{k}\mathrm{m}{\mathrm{h}}^{-1}$ and a ship $\text{B}$ $\text{100 km}$ south of $\text{A}$, is moving Northwards with a speed of $10\mathrm{ }\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ . The time after which the distance between them becomes shortest, is:

• A

  $0\mathrm{ }\mathrm{h}$
• Correct answer
  B

  $5\mathrm{ }\mathrm{h}$
• C

  $5\sqrt{2}\mathrm{ }\mathrm{h}$
• D

  $10\sqrt{2}\mathrm{ }\mathrm{h}$

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,

$\mathrm{t}=\frac{50\sqrt{2}}{10\sqrt{2}}=5\mathrm{h}\mathrm{r}\mathrm{s}$

Hence, the correct answer is option: 'B'.