Question

A 17-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away from the wall at a constant rate of 2 feet per second. How fast is the top of the ladder sliding down ?

Answer 1

To find the rate at which the top of the ladder is sliding down, use the Pythagorean theorem and differentiate the equation with respect to time.

Step-by-step explanation:

The problem involves a ladder leaning against a wall. We need to find the rate at which the top of the ladder is sliding down when the bottom of the ladder is sliding away from the wall at a constant rate of 2 feet per second.

Let's denote the distance between the bottom of the ladder and the wall as x, and the distance between the top of the ladder and the wall as y. We can use the Pythagorean theorem to relate x and y: x^2 + y^2 = 17^2.

Differentiating both sides of the equation with respect to time, we get: 2x(dx/dt) + 2y(dy/dt) = 0.

Substituting the given values, we can solve for dy/dt, which represents the rate at which the top of the ladder is sliding down.