Special Relativity: Conservation of Energy + Momentum?

[mintsnapple]

Homework Statement

Homework Equations

Energy of a moving particle = γmc^2
Momentum of a moving particle = γmv

The Attempt at a Solution

I feel like there is something wrong here...I know I'm supposed to find the VERTICAL component of velocity, but can the total velocity really be the same?

 

[voko]

Velocity and momentum are vectors. The picture clearly shows that those vectors have different directions. You cannot denote them both by the same symbol $v$ and treat them as equal.

 

[voko]

Besides, the gamma factors before and after decay are not equal.

 

[Chestermiller]

You need to write the momentum balances in the x- and y- directions, and also for the time components. Note that the sum of the masses of the final particles is less than the original particle. This will come into play in the time component balance.

 

[hjelmgart]

There is supposed to be conservation of momentum in both x and y direction. The total momentum in y is zero, as it has no initial component in the y-axis.