Solving a falling ladder problem using related rates

The video tutorial explains a problem involving a ladder leaning against a wall. The base of the ladder is pulled away from the wall at a rate of 3 feet per second, and the task is to determine how fast the top of the ladder is falling when the base is 30 feet from the wall. The instructor uses the Pythagorean theorem to relate the lengths and differentiates the equation with respect to time to find the rate of change. The solution involves calculating the rate at which the top of the ladder falls, resulting in a negative 9.4 feet per second.

What equation is used to relate the base, height, and length of the ladder?

What is the instantaneous rate of change of the height of the ladder?

What is the final rate at which the top of the ladder is falling when the base is 30 feet from the wall?