Maximum Angle of a Simple Pendulum with Given Parameters

[Carrie]

Homework Statement

A simple pendulum of length 2.00 m is made with a mass of 2.00 kg. The mass has a speed of 3.00 m/s when the pendulum is 30.0° above its lowest position.

(a) What is the maximum angle away from the lowest position the pendulum will reach?

Homework Equations

1/2mv^2(initial) + mgh(initial) = 1/2mv^2(final) + mgh (final)

The Attempt at a Solution

1/2mv^2(initial) + mgh(initial) = 1/2mv^2(final) + mgh (final)

1/2(2)(3)^2 + (2)(9.8)(2)cos(30) = 1/2(2)(0)^2 + (2)(9.8)(2)cos(theta)
And solving for theta, I get some imaginary number or something. I can't figure out what I'm doing wrong, or maybe I just messed up from the beginning.

Thanks!

 

[Simon Bridge]

Draw a picture: the height is not $2\cos\theta$.

 

[Carrie]

Oh, oops! I got it now. Thank you!

 

[Simon Bridge]

Well done. Easy mixup to make.