# Incident kinetic energy

1. Nov 14, 2007

### wchvball13

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

A projectile (mass = 0.24 kg) is fired at and embeds itself in a target (mass = 3.00 kg). The target (with the projectile in it) flies off after being struck. What percentage of the projectile's incident kinetic energy does the target (with the projectile in it) carry off after being struck?

2. Relevant equations

½m1vf1² + ½m2vf2² = ½m1vo1² + ½m2vo2²

3. The attempt at a solution

I don't even know where to start if you don't have one of the velocities. Just point me in the right direction and hopefully I can take it from there. There aren't any examples in the book, or any explanations of how to do this.

I know that since the target is at rest to start off with the equation will be
½m1vf1² + ½m2vf2² = ½m1vo1² + 0
but that's all I got...

2. Nov 14, 2007

### Shooting Star

You used conservation of KE. But part of the original KE of the projectile may be dissipated as heat, sound etc. But momentum is always conserved. So, use initial linear momentum equal to final linear momentum.

You do know the initial velo of the target. Assume v1, v2 etc. Finally they'll cancel out.

3. Nov 15, 2007

### wchvball13

so this is the equation I want?

m1vf1 + m2vf2 = m1vo1 + 0

and then just cancel out the velocities? I'm so confused

4. Nov 15, 2007

### Shooting Star

The target was stationary, so its velo was zero. Suppose the projectile had velo v1 and mass m and mass of target is M. Then, initial momentum = mv1 + 0.

After impact, they stick together and suppose go off with velo v. Then final momentum is (m+M)v.

So, mv1+0=(m+M)v. -(1)

(v and v1 are unknowns. But since they want a ratio only, they’ll cancel out, as we’ll see.)

Next, you know the initial KE of projectile, and also the final KE of the combined masses.

Final KE/Initial KE = ((m+M)v^2/2)/(mv1^2/2). -(2)

Now put in values of v/v1 from (1) in terms of M and m in (2).

Can you do the last step and convert into %age?