Pion Decay into Gamma rays angle

[cooev769]

So i have a question regarding a homework question I'm working on which suggest a neutral pion traveling with velocity v decays into two gamma rays of equal theta to the normal and they of course have velocity c. It then asks to prove that

v= cos theta

Which kind of confuses me. I mean if we assume that the gamma rays travel off at an angle and the distance they travel in time t is at a right angle to the distance the pion would have traveled at velocity v, we can form a right handed triangle with adjacent length vt and hypotenuse ct, but how can we just assume that you can just go north of vt and it will find ct right at the end of the hypotenuse and hence use this trigonometric rule.

Thanks.

 

[cooev769]

Oh wait is it due to conservation of momentum so the vertical components of the c's must cancel and therefore the horizontal components must be the same length? Cheers.

 

[mfb]

Oh wait is it due to conservation of momentum so the vertical components of the c's must cancel and therefore the horizontal components must be the same length? Cheers.

Exactly.