Relativistic Momentum of a particle of mass

[Sierevello]

Homework Statement

A particle of mass m(naught) moves through the lab at .6c. Suddenly it explodes into two fragments. Fragment 1 has mass .66m(naught) and moves at .8c in the same direction as the original particle had been moving. Determine the velocity (magnitude and direction) and mass of fragment 2?

Homework Equations

m = m(naught) / sqrt (1-(v^2/c^2)
p = m(naught) v(naught) / sqrt (1-(v^2/c^2)

The Attempt at a Solution

I have worked this problem for the last 3 hours. I am not sure how to find the mass of the 2nd particle and also everytime I work the problem I get a nonsense answer. I understand that momentum is conserved and initial energy = final energy. I was trying to use

p total = p piece 1 + p piece 2 where p is the relativistic momentum.

The m(naught) is throwing me off also.

Thansks for any help.

 

[diazona]

What you denote as "m" is something called relativistic mass, which is becoming an outdated concept. I would suggest dealing only with the invariant mass, which you currently call "m(naught)" and many other people just call "m". So your formula for momentum becomes
$$p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}}$$
and there is no need for anything to be called "m(naught)"

Anyway, you have a formula for momentum of a high-velocity particle. What's the formula for energy of a high-velocity particle? Once you have that, use the fact that total momentum is conserved in a collision, and total energy is also conserved. So compute the total momentum before and after the collision and set them equal to each other; also, compute the total energy before and after the collision and set them equal to each other.

If you get stuck after that, post your work here so we can point out any mistakes.