A ladder 50ft ling is leaning against a house. The base of the ladder is being pulled at 1ft/sec. How fast is the ladder moving down when the base is 30ft

Answer 1

I'm sorry, but this uses a little Calculus...

We know this is a 3-4-5 triangle ==> .

The dimensions, when the base is 30 ft from the wall are: 30, 40, 50

So, the top of the ladder if 40 feet up. The length of the ladder is fixed at 50.

The length of the ladder is the hypotenuse of the triangle and does NOT change with time.

We know: x^2 + y^2 = hypotenuse^2

Use calculus and differentiate both sides

2x(dx/dt) + 2y(dy/dt) = 0

When x = 30 and y = 40, we get:

2(30)(1 ft/sec) + 2(40)(dy/dt) = 0

60 + 80(dy/dt) = 0

dy/dt = -60/80

dy/dt = -.75 ft/sec.

So, the top of the ladder is sliding down at a rate of .75 ft/sec.