# Momentum and kinetic energy in collisions with a bullet

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

A bullet of mass 4.2 g strikes a ballistic pendulum of mass 2.0 kg. The center of mass of the pendulum rises a vertical distance of 18 cm. Assuming that the bullet remains embedded in the pendulum, calculate the bullet’s initial speed.

**2. Relevant equations**

**3. The attempt at a solution**

I started by converting everything into the correct units:

Bullet’s mass(m)= 0.0042 kg Ballistic pendulum(M)= 2 kg Vertical distance(h)= 0.18 m

Then used this equation to solve for the velocity of the bullet after the collison:

v_{bullet}=[itex]\sqrt{2gh}[/itex]

v_{bullet}=[itex]\sqrt{2(9.8)(0.18)}[/itex]

v_{bullet}=1.878 m/s

Then this equation to get the bullet’s initial speed:

v_{i}=[itex]\frac{(M+m)}{m}[/itex](V)

v_{i}=[itex]\frac{(2+0.0042)}{0.0042}[/itex](1.878)

v_{i}=896.16 m/s

I’m not sure what I’m doing wrong, my online homework only wants 2 significant digits.

Also, if someone could explain to me where these equations came from I would really appreciate it. I’m having some trouble understanding how to manipulate the energy equations to wind up with the ones I used in the problem.

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