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## Homework Statement

A mass of 3.50 kg is suspended from a 1.59 m long string. It revolves in a horizontal circle as shown in the figure.

The tangential speed of the mass is 2.99 m/s. Calculate the angle between the string and the vertical.

## Homework Equations

a_c = v^2/r

F = m*a_c

tanθ=sinθ/cosθ

sin^2θ=1-cos^2θ

## The Attempt at a Solution

Vertical: T*cos(θ)-m*g=0 → T=(m*g)/cos(θ)

Horizontal: T*sin(θ) = m*a_c

Combined the two: ((m*g)/cos(θ))sin(θ)=m*a_c → m*g*tan(θ)=m*a_c → g*tan(θ)=a_c

we know that a_c=v^2/r, plug that in to get g*tan(θ)=v^2/r

r=L*sin(θ) → g*tan(θ)=v^2/(L*sin(θ))

I cannot get past this point and the notes on the problem say that a quadratic equation needs to be solved at some point.