question_answer

Ship is sailing towards north-east with velocity \[\vec{v}=30\hat{i}+50\hat{j}\] where \[\hat{i}\] points east and \[\hat{j},\] north. Ship B distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. will be at minimum distance from B in:

A) 4.2 hrs

B) 2.2 hrs

C) 2.6 hrs  

D) 3.2 hrs

Correct Answer: C

Solution :

\[{{\vec{V}}_{AB}}=40\hat{i}+50\hat{j}\] \[{{\vec{r}}_{BA}}=150\hat{j}\] \[{{t}_{\min }}=\frac{\left| {{{\vec{V}}}_{AB}}\centerdot {{{\vec{r}}}_{BA}} \right|}{{{\left| {{{\vec{V}}}_{AB}} \right|}^{2}}}=2.6hrs.\]