An unstable particle is at rest and suddenly breaks up into two fragments. No ex

Question

An unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.780c and a mass of 1.27 10-27 kg, while the other has a mass of 4.61 10-27 kg. What is the velocity of the more massive fragment?
Can you workout very part of this problem please! An unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.780c and a mass of 1.27 10-27 kg, while the other has a mass of 4.61 10-27 kg. What is the velocity of the more massive fragment?
Can you workout very part of this problem please!
Can you workout very part of this problem please!

Explanation / Answer

Use conservation of relativistic momentum. Assuming the initial particle was at rest and the given masses are rest masses, you have;
P1 = P2 = P

First calculate "P" from the given info on the lighter particle, say, m1;
P = m1v1/SQRT[1 - (v1/c)^2]

Once you get a number for "P" , set it equal to "P2" (heavier fragment) and solve for "v2"
P = m2v2/SQRT[1 - (v2/c)^2]
v2 = Pc/SQRT[(m2c)^2 + P^2]

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