A 31 ft ladder leaning against a wall begins to slip with the base moving at a rate of 5 (ft)/s . How fast is the top of the ladder moving at the moment the top of the ladder is 10 ft above the ground

Question

Please help me answer this question

Answer 1

Let x be the horizontal distance from the base of the ladder to the wall. Let y be the vertical distance from the base of the wall to the top of the ladder. x and y are the legs of a right triangle and are related in this way:

x² + y² = 31² ; y = 10 , x = √861 , dx/dt = 5 , dy/dt = ?

2x·dx/dt + 2y·dy/dt = 0

10√861 + 20 dy/dt = 0

dy/dt = - √861 / 2 ft/sec