JEE Main 2014 Mathematics question
Two ships A and B are sailing straight away from a fixed point O along routes such that ∠AOB is always 120°. 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 ):
Answer: (1)
Solution
By the cosine rule with , AB^2 = OA^2 + OB^2 + OA\cdot OB. At the given instant , so . Differentiating,
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