Question

A Sixteen Foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?
The Top of the ladder is moving down at a rate of ___feet/second when the foot of the ladder is 5 feet from the wall.

Answer 1

Answer: The top of the ladder is moving down at a rate of 0.66 feet/second when the foot of the ladder is 5 feet from the wall

Step-by-step explanation: Please see the attachments below

Answer 2

Answer:

-0.69 feet per second

Step-by-step explanation:

We have dx/dt = 2 ft/sec, and we want to determine dy/dt.

x and y are related by the Pythagorean Theorem.

x²+y²=16²

Differentiate both sides of this equation with respect to t to get

$2x\frac{dx}{dt}+2y\frac{dy}{dt} =0$

$2y\frac{dy}{dt} =-2x\frac{dx}{dt}$

Divide both sides by 2y

$\frac{dy}{dt} =-\frac{x}{y}\frac{dx}{dt}$

When x = 5 ft, we have

x²+y²=16²

5²+y²=256

y²=256-25=231

therefore

y= $\sqrt{213}$

$\frac{dy}{dt} =-\frac{5}{\sqrt{213}}\frac{2 ft}{sec}$

=-0.69

The top of the ladder is sliding down (because of the negative sign in the result) at a rate of -0.69 feet per second.