# A simple pendulum swinging

1. Dec 6, 2015

### Carrie

1. The problem statement, all variables and given/known data
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?

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

3. 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!!

2. Dec 6, 2015

### Simon Bridge

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

3. Dec 6, 2015

### Carrie

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

4. Dec 6, 2015

### Simon Bridge

Well done. Easy mixup to make.