What Is the Final Velocity at the Highest Point of a Pendulum?

[warfreak131]

Edit: sorry, i meant a problem concerning kinetic and potential energy :)

Homework Statement

http://img136.imageshack.us/img136/8787/diagramln.jpg

A mass on a pendulum with length L has a velocity of $$\sqrt{2gL}$$ at it's lowest point. At it's lowest point, the string hits a pole at a distance of .8L sticking out of the wall. What is it's velocity when it reaches its highest point?

Homework Equations

$$KE_{bottom} = PE_{top}+KE_{top}$$

The Attempt at a Solution

The distance between the pole and the bottom is .2L, so the height at the top is .6L.

Since it has a velocity and a height at the top, it has both kinetic and potential energy. The potential energy at the bottom of the pendulum is 0. So I thought:

$$\frac{1}{2}m{v^2}_{bottom} = mg(.6L)+\frac{1}{2}m{v^2}_{top}$$
$$\frac{1}{2}2mgL = m(.6gL+\frac{v^2}{2})$$
$$gL = .6gL+\frac{v^2}{2}$$
$$.4gL = \frac{v^2}{2}$$
$$.8gL = {v^2}$$
$$\sqrt{.8gL} = v$$

but the book says the answer is $$\sqrt{1.2gL}$$

 

[rl.bhat]

In the first equation replace mg(0.6L) by mg( 0.4L).