# pully question

• Jan 9th 2007, 12:03 PM
math619
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? :confused:

Can anyone help out with this one? It's really bothering me.
Thx
• Jan 9th 2007, 12:52 PM
galactus
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.

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

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