A ladder feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of feet per second. How fast is the top of the ladder moving down the wall when its base is feet from the wall? Round your answer to two decimal places.
A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec

Question

A ladder  feet long is leaning against the wall of a house (see figure). The base of the ladder is pulled away from the wall at a rate of  feet per second. How fast is the top of the ladder moving down the wall when its base is  feet from the wall? Round your answer to two decimal places. 
A) ft/sec 
B) ft/sec 
C) ft/sec 
D) ft/sec 
E) ft/sec

Quizplus · Accepted Answer

We can use the Pythagorean Theorem to set up an equation relating the distance from the wall (x) to the height up the wall (y): x^2 + y^2 = 11^2. Differentiating both sides with respect to time, we get:
2x(dx/dt) + 2y(dy/dt) = 0
Simplifying and plugging in x = 11 and dx/dt = 11, we get:
(11)(11) + 2(11)(dy/dt) = 0
Solving for dy/dt, we get:
dy/dt = -121/22 ≈ -5.50
The negative sign indicates that the ladder is sliding down the wall. Rounding to two decimal places, the answer is 11eaa595_6617_8982_a696_9d584b0f18fd_TB4584_11_TB4584_11 ft/sec.

A Ladder Feet Long Is Leaning Against the Wall