Homework SourseA 10 foot ladder leaning against a wall is sliding in such a
A 10 foot ladder leaning against a wall is sliding in such a way that its base is sliding away from the wall with rate of 5 inches/second. Find the corresponding rate of change of the top in the vertical direction when the top of the ladder is 2 feet above the ground.
Solution
we have, x^2 + y^2 = 10^2 ( from Pythagores theorem) now, differentiating , we have, 2x ( dx/dt) + 2y(dy/dt) = 0 x ( dx/dt) + y(dy/dt) = 0 now, when y = 2 x = [10^2 - 2^2]^0.5 = 9.79796 now, 9.79796 x 5 = 2 (dy/dt) dy/dt = 24.495 in/sec
