Circular motion: find velocity with angle, mass, and radius

[ecalop]

This was a homework problem; after five tries, I still did not get it, and I can't figure out how to get at the answer the assignment gave me. I could not find the answer anywhere that didn't get into angular velocity, which we are not at yet (and also did not give me the answer!).

1. Problem
How fast do you need to swing a 200-g ball at the end of a string in a horizontal circle of 0.6-m radius so that the string makes a 34∘ angle relative to the horizontal?

So we have:
mass: 0.2-kg (200-g)
radius: 0.6-m
angle: 34∘

Homework Equations

I have tried:
tan(34) = vy/vx, but that just got me dv, which was no help without time or period

tan(34) = v^2/r*g; this was wrong (and also did not take mass into account)

s = (v^2*sin(2*34))/g; I used the radius for s, which was a long shot, although this answer got me the closest (2.52 m/s)

m*(v^2/r) = +m*g + (-F), using grav in F=ma. obviously the acceleration was no gravity of Earth.

The Attempt at a Solution

The answer is apparently v=2.95 m/s

I have absolutely no idea how they got to this answer! I used any relevant-looking solution in the chapter this problem is from, I searched the web (including these forums), and no one else's problem had the solution. What was I doing wrong?

 

[Nathanael]

If the ball travels in a horizontal circle, what is the net vertical force on the ball? What is the net horizontal force? What forces are acting on the ball? (What would a FBD look like?)