Particle decay: Relativistic or classical?

[Isomorphism]

This question was asked in an competitive exam in India.

The relevant equations are momentum conservation in the classical sense and the 4 momentum conservation.

My attempt: Classical momentum conservation would seem inaccurate since the kinetic energies are high. However, a straightforward application of it yields option (a). I think it is wrong since we end up with more energy than we started with. Initial energy is 3GJ, but final energy is 10 GJ since C has 8GJ of energy.

I wanted to know how to solve it using special relativity. It looks like information about the masses is missing.(I know that I cannot use conservation of masses.) So I am wondering whether it is possible to solve this problem with relativistic corrections and whether the answer still remains 30 degrees.

Thanks,

 

[PeroK]

The following question was asked in an competitive exam in India:https://www.physicsforums.com/attachments/108398

The relevant equations are momentum conservation in the classical sense and the 4 momentum conservation.

My attempt: Classical momentum conservation would seem inaccurate since the kinetic energies are high. However, a straightforward application of it yields option (a). I think it is wrong since we end up with more energy than we started with. Initial energy is 3GJ, but final energy is 10 GJ.

I wanted to know how to solve it using special relativity. It looks like information about the masses is missing.(I know that I cannot use conservation of masses.) So I am wondering whether it is possible to solve this problem with relativistic corrections and whether the answer still remains 30 degrees.

Thanks,

It's got nothing to do with Relativity. The piece that went off at right angles should have $1 GJ$ not $2 GJ$.

 

[Isomorphism]

How did you know that it is a classical momentum problem apriori?

The energies of the two pieces are 8GJ and 2GJ.

I have updated my original post.

It's got nothing to do with Relativity. The piece that went off at right angles should have $1 GJ$ not $2 GJ$.

 

[PeroK]

How did you know that it is a classical momentum problem apriori.

The energies of the two pieces are 8GJ and 2GJ.

If it was a SR problem, it would have said "relativistic velocity", not "high velocity".

 

[vela]

How did you know that it is a classical momentum problem apriori?

1 GJ might sound like a lot, but if you calculate the equivalent amount of mass, you find $m = \frac{10^9}{(3\times10^8)^2}= 1.1\times 10^{-8}\text{ kg}.$ The mass of the missile is many orders of magnitude above that.

 

[PeroK]

1 GJ might sound like a lot, but if you calculate the equivalent amount of mass, you find $m = \frac{10^9}{(3\times10^8)^2}= 1.1\times 10^{-8}\text{ kg}.$ The mass of the missile is many orders of magnitude above that.

Or, if the missile had a mass of $1 kg$ then its velocity would be less than $8 \times 10^4 m/s$

 

[Isomorphism]

Thanks for that clarification.

If it is classical, how has the total energy increased?

 

[PeroK]

Thanks for that clarification.

If it is classical, how has the total energy increased?

That would be a mistake in the question, as pointed out in post #2.