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

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10 $\sqrt{2}$ h

5 $\sqrt{2}$ h

answer is D.

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Detailed Solution

$\begin{array}{l} V_{A} = 10 (- \hat{i}); V_{B} = 10 (\hat{j}); V_{BA} = 10 \hat{j} + 10 \hat{i}; \\ V_{BA} = 10 \sqrt{2} km / h \end{array}$
$V_{A} = - 10 \hat{i}$

Time taken to reach the shortest distance between A and B
$= \frac{OB}{V_{BA}} = \frac{50 \sqrt{2}}{10 \sqrt{2}} = 5 h$

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