A shell explodes into two identical fragments; find v

[toboldlygo]

Homework Statement

[/B]
A shell of mass m and speed v explodes into two identical fragments. If the shell was moving horizontally (the positive x direction) with respect to Earth, and one of the fragments is subsequently moving vertically with speed v, find the velocity v of the other fragment immediately following the explosion. (Use the following as necessary: v.)

Homework Equations

conservation of momentum: m_1iv_1i= 0.5m_1fv_1f+0.5m_2fv_2f

The Attempt at a Solution

So, what I did was set mv=.5mv+.5mv. Solving for v, I get v=v. I don't know what I'm doing wrong here. I'm pretty sure I'm supposed to be using the conservation of momentum equation, but I don't know where I'm going wrong. Thanks in advance for any help!

 

[haruspex]

set mv=.5mv+.5mv.

Velocity and momentum are vectors. Your notation is very unclear, but it seems to me that on the right there you are adding momenta in two different directions as though they are scalars.
Consider horizontal and vertical momentum separately.

 

[toboldlygo]

Velocity and momentum are vectors. Your notation is very unclear, but it seems to me that on the right there you are adding momenta in two different directions as though they are scalars.
Consider horizontal and vertical momentum separately.

Oh wow, that simplifies things so much. Thank you! Even though I've been using vectors for well over five weeks now I completely forgot.