JEE Main 2014 · 11 Apr · Shift 1 · Mathematics Q73

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MathematicsSingle correct+4 / -1Question 73 of 90

Two ships A and B are sailing straight away from a fixed point O along routes such that $\angle AOB$ 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) :

260/\sqrt{37}

260/37

80/\sqrt{37}

80/37

Answer and worked solution

Official answer: A

With $a=OA$ , $b=OB$ and the angle at 120°: $s^2=a^2+b^2+ab$ . Now $s=\sqrt{64+36+48}=2\sqrt{37}$ . Differentiating,
$2s\dot s=2a\dot a+2b\dot b+\dot ab+a\dot b=320+360+120+240=1040.$
$\dot s=\frac{1040}{4\sqrt{37}}=\frac{260}{\sqrt{37}}\text{ km/hr}.$

Topics:Rate of change

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JEE Main 2014 · 11 Apr · Shift 1, Mathematics question 73