please help me with a physics question! what is the speed....?

Question

An unstable particle at rest breaks up into two fragments of unequal mass. The mass of the lighter fragment is 2.40 x10-28 kg, and that of the heavier fragment is 1.64 x10-27 kg. If the lighter fragment has a speed of 0.893c after the breakup, what is the speed of the heavier fragment?
Thank you very much for any help you can give me on this question! I really appreciate it!

Answer 1

Conservation of RELATIVISTIC momentum.

momentum of fragment = (gamma)(m)(v)

where (gamma) = sqrt(1/(1-(v/c)^2))

If v is small compared to c, gamma is nearly 1, so you can use the simple formulas like the answers above did. In this case, that will not work.

Calculate that momentum. So the other fragment must have the same magnitude of momentum. So you can find its speed using the same relativistic formula.

Part (b) of this question that they will ask is to find the original particle mass. To do that, use conservation of energy.

E = sqrt (m^2 c^4 + p^2 c^2)
You know the final masses and momenta, so you can find energy. Initially, the particle has no momentum, so its energy is just E = mc^2. Solve for m.

Answer 2

We use the conservation of momentum, Thus, if the light fragment is ml and the heavy fragment is mh, ml x vl = mh x vh. You know everything except vh.

BTW, there is a difference between "speed" in physics and "velocity". If there wasn't, you couldn't solve this problem. Be careful