# a 25-foot ladder is leaning against a house. the base of the ladder is pulled away from the house at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when the...

a 25-foot ladder is leaning against a house. the base of the ladder is pulled away from the house at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when the base is

a)7 feet

b)15 feet

c) 24 feet

from the house?

justaguide | Certified Educator

The length of the ladder is 25 feet. It is leaning against the wall of a house. The base of the ladder is pulled away from the wall at 2 feet per second. Let B the distance of the base of the ladder from the wall. If H is the height of the top of the ladder, `H^2 + B^2 = 25^2`

Take the derivative with respect to time of both the sides.

`2*H*((dH)/(dt)) + 2*B*((dB)/(dt)) = 0`

`(dB)/(dt) = 2`

=> `(dH)/(dt) = -2*B`

When B = 7 feet, `(dH)/(dt)` = -14 ft/s. When B = 15, `(dH)/(dt)` = -30 and when B = 24 ft/s, `(dH)/(dt)` = -48 ft/s.

The top of the ladder is moving down at 14 ft/s, 30 ft/s and 48 ft/s when the base is 7 ft, 15 ft and 48 ft respectively.