Frictionless Bead Sliding Down A Parabola

[devon cook]

Homework Statement

It seems simple, doesn't it? A bead starts from (0,1/2) and simply slides down the parabola y=(1/2)(x-1)2 under gravity. The problem is to get its position rel. to origin in terms of time, ie.
r = [x(t),y(t)]. Anyone into this?

Homework Equations

y' = x-1 = tan A where A is angle tangential veloc. (v) (and tang. accel.(a)) makes with x axis.
a = -g sin A .

The Attempt at a Solution

For starters, can I say that sin A = -(x-1)/sqr(1+(x-1)^2) ?

 

[WiFO215]

What quantities do you think are conserved? Can you use them?