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 ):

Step-by-step solution

Let OA =x ~km , OB =y ~km , AB = R ( AB )^2=( OA )^2+( OB )^2-2( OA )( OB ) 120^ R ^2=x^2+y^2-2 x y (- 1 2 )=x^2+y^2+x y R at x=6 ~km , and y=8 ~km R = 6^2+8^2+6 8 =2 37 Differentiating equation (1) with respect to t gathered 2 R d R d t =2 d x d t +2 y d y d t + (x d y d t +y d x d t ) = 1 2 R [2 8 20+2 6 30+(8 30+6 20)] d R d t = 1 2 2 37 [1040]= 260 37 gathered