# Bullet conservation of momentum problem

1. Jun 5, 2014

### BrainMan

1. The problem statement, all variables and given/known data
A 7-g bullet is fired into a 1.5-kg ballistic pendulum. The bullet emerges from the block with a speed of 200 m/s, and the block rises to a maximum height of 12 cm. Find the initial speed of the bullet.

2. Relevant equations
conservation of momentum

3. The attempt at a solution
First I tried to find the initial momentum of the bullet as if it did't penetrate the block
so .007vi = (1.507)vf
because I have two unknowns I used the conservation of mechanical energy to solve for vf
1/2(1.507)(vf2) = (1.507)(9.8)(.12)
vf = 1.54 m/s
then plug that in to find the initial velocity
vi = 435.29 m/s
initial momentum = 3.05

Then I tried to find the momentum of the bullet exiting the block and add it to the initial momentum to get the total initial momentum.
200(.007) = 1.4
1.4 + 3.05 = 4.45
and finally I divided that by the mass to get the initial velocity 635.75 m/s. The correct answer is 529 m/s.

2. Jun 5, 2014

### Nathanael

How did you get this number?

From this? (If yes, then double check your numbers.)

3. Jun 5, 2014

### Nathanael

Other than that, looks good!

P.S.
You should not round your numbers until the very end. (Try to solve the problem with just algebra and then plug in the numbers at the end.) The reason is that your answer will be slightly off.

(In this problem and another you've recently posted, you rounded before the end which caused your answers to be off by about half a percent, which isn't much, but in some problems rounding before the end will cause you to be off by more than half a percent, and in other problems half a percent could be a meaningful error.)

4. Jun 5, 2014

### BrainMan

OK I see what I did! Thanks!