How Much Kinetic Energy Does the Target Retain After Collision?

[wchvball13]

Homework Statement

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?

Homework Equations

½m1vf1² + ½m2vf2² = ½m1vo1² + ½m2vo2²

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...

 

[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.

 

[wchvball13]

so this is the equation I want?

m1vf1 + m2vf2 = m1vo1 + 0

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

 

[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?