# Relativistic energy of particle of mass

1. Sep 11, 2009

### w3390

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

A particle of mass M decays into two identical particles each of mass m, where m = 0.3M. Prior to the decay, the particle of mass M has a total energy of 5Mc2 in the laboratory reference frame. The velocities of the decay product are along the direction of motion M. Find the velocities of the decay products in the laboratory reference frame.

2. Relevant equations

Etot=$$\frac{mc^2}{\sqrt{1-\frac{u^2}{c^2}}}$$

3. The attempt at a solution

Since I am given the total energy to be 5Mc^2 in the frame of the laboratory, I plugged it into the above equation and solved for u. I get u to be .9798c. I have also found the velocities of the particles in the frame of the initial particle to be +/-.8c. However, when I do the velocity transformation, I get the faster particle to be moving .99c and the slower particle to be moving .83c relative to the laboratory, but my online hw is saying these answers are wrong. Can anybody help me figure out where I am going wrong? I am comfortable with my velocity transformation mathematics, so I figure the mistake is with the velocity of the particle of mass M.

2. Sep 11, 2009

### gabbagabbahey

Could just be a rounding error....how many sig-digs are your final results supposed to be?

3. Sep 12, 2009

### w3390

You're right. I ended up getting one of the answers wrong because I input .833c instead of .832c when the problem only gave one number with one significant figure. Thanks though.