JEE Mains · Maths · STD 12 - 6. Application of derivatives
Two ships \(A\) and \(B\) are sailing straight away from a fixed point \(O\) along routes such that \(\angle AOB\) is always \(120^o\) . At a certain instance, \(OA\, = 8\, km\), \(OB\, = 6\, km\) and the ship \(A\) is sailing at the rate of \(20\, km/hr\) while the ship \(B\) sailing at the rate of \(30\, km/hr\). Then the distance between \(A\) and \(B\) is changing at the rate (in \(km/hr\))
- A \(\frac{{260}}{{\sqrt {37} }}\)
- B \(\frac{260}{37}\)
- C \(\frac{{80}}{{\sqrt {37} }}\)
- D \(\frac{80}{37}\)
Answer & Solution
Correct Answer
(A) \(\frac{{260}}{{\sqrt {37} }}\)
Step-by-step Solution
Detailed explanation
Let \(OA=x km\), \(OB=y km\), \(AB=R\) \({\left( {AB} \right)^2} = {\left( {OA} \right)^2} + {\left( {OB} \right)^2} - 2\left( {OA} \right)\left( {OB} \right)\cos {120^o}\)…
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