A rod A B, 13 feet long moves with its ends A and B on two perpendicular lines O X and O Y respectively. When A is 5 feet from O , it is moving away at the rate of 3 feet / sec . At this instant, B is moving at the rate

Step-by-step solution

Note that OAB is a right angled triangle. Let OA =x ft and OB =y ft . y^2=169-x^2 Now, differentiating above function w.r.t. time 't', we get 2 y d y dt =-2 x d x dt At x=5, d x dt =3 ft / sec ... [Given] Also, at x=5, y=12 (i) 2(12) d y dt =-2(5)(3) d y ~d x = -5 4 Negative sign indicates that B is moving downwards. B is moving at the rate 5 4 ft / sec downwards.