question_answer

 A ship A is moving Westwards with a speed of \[10\text{ }km\text{ }{{h}^{-1}}\] and a ship B 100 km South of A, is moving Northwards with a speed of \[10\text{ }km\text{ }{{h}^{-1}}\]. The time after which the distance between them becomes shortest, is

A) 5h                    

B) \[5\sqrt{2}\,\,h\]

C) \[10\sqrt{2}\,h\] 

D) 0 h

Correct Answer: A

Solution :

\[{{V}_{A}}=10\left( -\widehat{i} \right)\] \[{{V}_{B}}=10\left( -\widehat{j} \right)\] \[{{V}_{BA}}=10\widehat{j}+10\widehat{i}\] \[=10\sqrt{2}\text{ km/h}\] \[\text{Distance OB=100 cos45}{}^\circ \] \[\text{=50}\sqrt{2}\text{ km}\]