Question

The top of a 19 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second. How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 12 feet away from the base of the wall?

Answer 1

Can you apply pythagorean theorem with the ladder is hypo. side?

Answer 2

Let x be the distance from the bottom of the ladder to the bottom of the
wall.
Let y be the distance from the top of the ladder to the bottom of the
wall.


\[ x^2 + y^2 = 19^2\\
2 x \frac{dx}{dt} + 2 y \frac{ dy}{dt} =0\\
x \frac{dx}{dt} + y \frac{ dy}{dt} =0\\
12 \frac{dx}{dt} + \sqrt{19^2-12^2}( -4) =0\\
\]
Solve for
\[
\frac{dx}{dt}= \frac{\sqrt{217}}{3}
\]