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## Homework Statement

With this problem I have to get the answer: cosθ = r/L * cosα - √(3)/2 * (1 - r/L)

which in other words mean I need to find angle θ with arccos[r/L * cosα - √(3)/2 * (1 - r/L)].

Here's the picture:

Lcosθ is the vertical length of the string at its lowest point.

rcosα is a fraction of that same vertical string in terms of displacement "r" (which is from the start of the string to the peg)

∠β is the angle between the peg and the horizon.

(L-r) sinβ is the height from the end of the peg and the horizontal

(L-r) cosα is the horizontal length of that same peg.

(L-r)cosα is the vertical length of the string from the ball to the peg.

So, this is not really a physics issue but more like a math issue but since this is a physics problem I've decided to put it under here.

My problem is that I am unable to continue from this point as shown on the picture of my attempt. I don't know where to continue from here on out. I am trying to find "t" for the equation but I am unsure how. Where do I continue from now?

## Homework Equations

[/B]

Newtonian Position Formula:

y

_{f}= y

_{i}+v

_{iy}t + .5gt

^{2}

x

_{f}= x

_{i}+v

_{ix}t + .5gt

^{2}

Energy Equation:

Work of hand - force of friction * displacement = delta Kinetic Energy + delta Potential Energy

W

_{h}- f

_{F}*d = [.5*mv

_{f}

^{2}- .5*mv

_{i}

^{2}] - [mgh

_{f}- mgh

_{i}]

## The Attempt at a Solution

Picture of Attempt: