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A ship A is moving west wards with a speed of $10 k m h^{- 1}$ and a ship $B$ $100 k m$ south of $A$ , is moving north wards with a speed of $10 k m h^{- 1}$ . The time after which the distance between them becomes shortest,is

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$5 \sqrt{2} h$

$10 \sqrt{2} h$

$5 h$

$0 h$

answer is C.

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Detailed Solution

$V_{A} = - 10 \hat{i}; V_{B} = 10 \hat{j}$

$V_{A} - V_{B} = - 10 \hat{i} - 10 \hat{j}$

$θ = 45^{0}, x = \frac{100}{\sqrt{2}} km$

$v_{rel} = 10 \sqrt{2} km$

$t = \frac{x}{v_{r e l}} = \frac{100 / \sqrt{2}}{10 \sqrt{2}} = \frac{100}{2 \times 10} = 5 hrs$

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