Speed of a disc after a collision

[Pochen Liu]

Homework Statement

I understand that if the change in impulse is 0.25, that because disc B is originally stationary the momentum disc B will have is equal to the impulse.

My question is how do we do this in terms of change in momentum?

Homework Equations

ΔP = Pf - Pi
P = mv

The Attempt at a Solution

ΔP = Pf - Pi
0.25 = Pf - (0.517 * 1.21)
Pf = 0.87557

Ps of the system = 0.62557
Ps = Pa + Pb = 0.87557 + Pb = 0.62557
Pb = -0.25
vb = -0.365

Why does this approach give the negative version of the answer?
I know what I've done isn't quite right because (Ps = Pa + Pb = 0.87557 + Pb = 0.62557) essentially states somehow the momentum in the system has increased with no external torque.

 

[haruspex]

0.25 = Pf - (0.517 * 1.21)

Momentum is a vector. You cannot add and subtract quantities like this unless they are known to be in the same direction. From the diagram, it is clear that the initial velocity of A is at some angle to the impulse.

For part bi) you do not need to consider A at all. Just think about the info you have regarding B.

 

[neilparker62]

$$ \vec{P_{ai}} = \vec{P_{af}}+\vec{P_{bf}} $$ and since post collision trajectories are at right angles: $$ \lvert\vec{P_{ai}}\rvert^2 = \lvert\vec{P_{af}}\rvert^2+\lvert\vec{P_{bf}}\rvert^2 $$