Rifle shoots bullet into pendulum What am I doing wrong?

[WahooMan]

Homework Statement

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.

Homework Equations

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

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?

 

[Doc Al]

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?

Your work looks fine to me.

 

[Andrew Mason]

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?

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

 

[WahooMan]

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

 

[Andrew Mason]

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

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

 

[Doc Al]

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.

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