Posted by **Isiah** on Thursday, October 13, 2011 at 10:20pm.

A 23 foot ladder is leaning on a 6 foot fence. The base of the ladder is being pulled away from the fence at the rate of 7 feet/minute. How fast is the top of the ladder approaching the ground when the base is 6 from the fence? [Note: The ladder is protruding over the top of the fence.]

The top of the ladder is approaching the ground at the rate of____________ feet/minute. [Enter a positive number only.]

- Calculus -
**Steve**, Friday, October 14, 2011 at 11:53am
Let the ladder make an angle t with the ground.

Let the distance from the base of the fence = x

Let the end of the ladder be at height h.

tan(t) = 6/x

sin(t) = h/23

tan^2 = sin^2/cos^2

36/x^2 = (h/23)^2 / (1 - (h/23)^2)

flip it upside down:

x^2/36 = (1-h^2/529)/(h^2/529)

x^2/36 = 529/h^2 - 1

2x/36 dx = -2(529)/h^3 dh

when x = 6

tan(t) = 6/6 = 1

so, h = 23/√2

2(6)/36 * 7 = -2(529)/(23^3/2√2) dh

84/36 = -1058/4302 dh

dh = -9.49 ft/s

or,

9.49 ft/s downward

## Answer this Question

## Related Questions

- Calculus - A 17 foot ladder is leaning on a 6 foot fence. The base of the ladder...
- Calculus - A 25 foot ladder is leaning on a 9 foot fence. The base of the ladder...
- Math Calculus - The foot of a 30-foot ladder is being pulled away from a ...
- Calculus - Mr. Cook was painting Arvada West High School, standing on top of a ...
- Calculus - Mr. Cook was painting Arvada West High School, standing on top of a ...
- calculus - A 13 foot ladder leaning against a wall makes an angle of degree ...
- Calculus--Please Help! - A 13-foot ladder is leaning against a vertical wall. If...
- College Calculus - A 13-foot ladder is leaning against a vertical wall. If the ...
- Calculus Ab - A 26 foot step ladder is leaned up against a 30 foot building to ...
- Calculus - related rates: a ladder, 12 feet long, is leaning against a wall. if ...

More Related Questions