Momentum problem involving collision of two balls

[Joshpho]

Homework Statement

(It includes a diagram so I'm just going to link it)
#22 from Chapter 7 of the People's Physics Book (second to last page, with the table)
http://scipp.ucsc.edu/outreach/07Momentum.pdf

Homework Equations

p(i)=p(f)
p(f)x=m*v*cosin(theta) [I "made these up", so to speak, but it seems logical]
p(f)y=m*v*sin(theta)

The Attempt at a Solution

The main trouble I am is with b), finding the actual direction of the 2 kg ball. First, however, I wanted to verify my steps so far is correct...

The initial momentum should be 8kg*m/s by summing the individual, positive momentums of each ball. For the final momentum of the 3 kg ball, I obtained them like so...

We know the angle is 30 degrees and it has a velocity of 1 m/s, so we know
Momentum in the x direction = 3kg*1m/s*cosin(30) = 1.50
Momentum y = 3kg*1m/s*sin(30) = 2.60

So now I set up our conservation equation like so...

8 kg*m/s = (1.50+2.60)kg*m/s + p(2kg ball)

Is this correct so far?

 

[NoPoke]

momentum is a vector quantity. So does it make sense to sum the momenta of the two balls?

 

[Joshpho]

We know that the total momentum before compared to the final momentum has to be equal, so yes?

 

[NoPoke]

ok, so how do you add two vector quantities?

 

[Joshpho]

Finding the diagonal of the paralellogram they form? But this doesn't seem possible to do without knowing the direction of the 2kg ball first.

Also, you are allowed to add momentum quantities, right? I was taught you could do that at least, since they're both mass and speed.

 

[NoPoke]

momentum : mass speed and direction. When you add momenta together you must keep track of direction too. So yes you will be finding the diagonal of the parallelogram either explicitly or by keeping the components of the vector separate. Much like map directions where you can say go 1 mile East and 1 mile North or equivalently go 1.4 miles NorthEast. It works the other way too: Even though a bird can fly 1.4 miles due NE we may have to take the equivalent route by traveling 1 mile East and 1 mile North.

So what is your initial momentum for the two masses?