## Related Rates - A Falling Ladder

HELP

Above, a 16-ft ladder leans against a wall. You can move the blue point along the ground to see how the movement of the top of the ladder relates to the movement of the bottom of the ladder. To animate smoothly, click the blue dot then press and hold the arrow keys.

#### Explore

1. If the bottom of the ladder moves away from the wall at a constant rate, how would you describe the movement of the top of the ladder?
2. If `x` is increasing, is `dh/dt` positive or negative? Here `x` is the distance from the bottom of the wall to the bottom of the ladder, `h` is the distance from the bottom of the wall to the top of the ladder, and these quantities change as a function of time, `t`.
3. Suppose the bottom of the ladder is `5` ft from the wall at time `t = 0` and it slides away from the wall at a constant rate of `3` ft/s. Find the velocity of the top of the ladder at time `t = 1`.
4. Suppose the top of the ladder slides down at a constant rate of `4` ft/s. Calculate `dx/dt` when `h = 12`.