Rifle shoots bullet into pendulum What am I doing wrong?

1. Oct 20, 2009

WahooMan

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

A 30g rifle bullet traveling 220 m/s buries itself in a 3.0kg pendulum hanging on a 2.1m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum's maximum displacement.

2. Relevant equations

p=mv
K=1/2mv^2
Ug=mgy

3. The attempt at a solution

First, I found the momentum of the bullet:

p=mv
p=(0.03kg)(200m/s)
p=6.6kg*m/s

Then I found the velocity of the pendulum after the bullet hits it:

(6.6kg*m/s)/(3.03kg)=2.18m/s

After that I found the Kinetic Energy of the system just after the bullet hits the pendulum:
KE=1/2mv^2
KE=(1/2)(3.03)(2.18)^2
KE=7.19J

Then, because that Kinetic Energy transfers to Gravitational Potential Energy when the pendulum has reached its max height, I set the Kinetic Energy equal to Gravitational Potential Energy.

Ug=mgy
7.19J=(3.03kg)(9.80)(y)
y=0.24m

Using the length of the pendulum (2.1m) as the hypotenuse and (length of the pendulum - y=1.86m) as the y component, I used the Pythagorean Thereom to solve for the x component.

a^2+b^2=c^2
1.86^2+b^2=2.1^2
b^2=2.1^2-1.86^2
b=0.98m

So I got the x component to be 0.98m and the y component to be 1.9m, but MasteringPhysics says I'm wrong. What did I do wrong?

2. Oct 20, 2009

Staff: Mentor

Your work looks fine to me.

3. Oct 20, 2009

Andrew Mason

As Doc Al says, your approach is correct. However, displacement should be measured from its original rest position. That is probably why your answer is not jiving. Also, I get .97m for the x component.

AM

4. Oct 20, 2009

WahooMan

Did I not measure from the rest position? What would be the correct answer if I did? What exactly did I do wrong?

5. Oct 20, 2009

Andrew Mason

You are using 1.9m for the change in y. The block does not change its y position by that amount. You found that it changes by .24 m.

AM

6. Oct 21, 2009

Staff: Mentor

D'oh! Good catch, AM. (I wasn't paying attention. )