At what rate is the ladder moving away from the wall when the ladder hits the ground?

3 ft/sec.
The foot of the ladder begins to slide along the ground away from the wall at a constant rate of 3 ft/sec. In the diagram below, the distance from the wall to the foot of the ladder is represented by x, and y represents the distance from the ground to the top of the ladder.

How fast is the ladder sliding down the wall at that moment?

The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s.

How to calculate the top sliding rate of a ladder?

Let x be the horizontal distance, in feet, from the wall to the bottom of the ladder. Let y be the distance, in feet, from the ground to the top of the ladder. The problem tells us that at the moment of interest, when x = 8 ft, d x d t = 2 ft/sec. We’ll use these values only at the end of our solution. 2.

Why does a falling ladder have an acceleration?

The ladder has forces (gravitation and friction with the wall and the floor most importantly) acting on it, hence it should have acceleration (if those forces don’t balance out). We can’t figure the acceleration, because there is no information about the mass of the ladder and the materials that make up the ladder and the wall.

How to calculate angle change as ladder slides?

The answer is the Chain Rule. (Recall that that rate is $\\dfrac {dx} {dt} = 2$ ft/s in this problem.) Remember that $ heta$ and x are both functions of time t: the angle changes as time passes and the ladder’s x -position changes as the ladder slides down the wall. We could have captured this time-dependence explicitly by writing our relation as

When does the bottom of a ladder fall?

You’re on a ladder. The bottom of the ladder starts slipping away from the wall. Amidst your fright, you realize this would make a great related rates problem… Created by Sal Khan. This is the currently selected item.