# 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?

Asked on by elpony

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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.