Question: A $25$ foot ladder is resting against a wall so that the bottom of the ladder is $7$ feet from the wall. The bottom of the ladder starts slipping away from the wall at a rate of $1$ foot per second. How many feet per second is the top of the ladder sliding down the wall when it is $15$ feet above the ground?
I got $2w\frac{dw}{dt} + 2h\frac{dh}{dt}=0.$ I know $w$ and $h$ and the derivative of $w$ and that’s about it. Solving for $\frac{dh}{dt}$ gave me $-\frac{3}{4}$, although this is incorrect. What did I do wrong?
If you do decide to solve it, please state how you got the answer as well! Thank you!