
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

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:
$\displaystyle x^{2}+(13.51.5)^{2}=z^{2}$
$\displaystyle x^{2}+144=z^{2}$
Differentiate:
$\displaystyle 2x\frac{dx}{dt}=2z\frac{dz}{dt}$
When x=9, we can see that z=15.
$\displaystyle \frac{dz}{dt}=\frac{x}{z}\frac{dx}{dt}$
$\displaystyle \frac{dz}{dt}=\frac{9}{15}(\frac{8}{5})=\frac{24}{ 25} \;\ m/sec$