1. ## pully question

This is another confusing word problem where you need to have a good diagram to work off of.

A pully is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pully. One end of the rope is tied to the bucket and the other end dangles loosly to the ground. A construction worker holds the end of the rope at a constant height (1.5 m) and walks away from beneath the pully at 1.6 m/s. How fast is the bucket rising when he is 9 m away from the path of the rising cement bucket?

Can anyone help out with this one? It's really bothering me.
Thx

2. Like many of these related rates problems, it involves ol' Pythagoras.

Let z=the hypoteneuse of the triangle (the length of the rope).

By Pythagoras:

$\displaystyle x^{2}+(13.5-1.5)^{2}=z^{2}$

$\displaystyle x^{2}+144=z^{2}$

Differentiate:

$\displaystyle 2x\frac{dx}{dt}=2z\frac{dz}{dt}$

When x=9, we can see that z=15.

$\displaystyle \frac{dz}{dt}=\frac{x}{z}\frac{dx}{dt}$

$\displaystyle \frac{dz}{dt}=\frac{9}{15}(\frac{8}{5})=\frac{24}{ 25} \;\ m/sec$