How Do Ice-Skating Twins Illustrate Conservation of Momentum?

[johnchops32]

Hi there I am new to the forum and I have a HW assignment due at 1130 pm tonight, i know I am procrastinating :\ but physics is my weak point. I can not figure this question out if my life depended on it. Here it is:

Identical twins, each with mass 64.2 kg, are on ice skates and at rest on a frozen lake, which may be taken as frictionless. Twin A is carrying a backpack of mass 12.0 kg. She throws it horizontally at 3.50 m/s to Twin B. Neglecting any gravity effects, what are the subsequent speeds of Twin A and Twin B?

. They have the same mass, i know the masses should cancel correct? And we have to use the conservation of momentum . But can someone help me out ?

 

[Simon Bridge]

Do not assume masses will cancel. Assign letters to everything and work the conservation laws. Let the laws tell you what does and does not cancel out.

Pick a direction to be positive, since momentum is a vector. For each twin write down the momentum before and the momentum after and equate them. So for Alice (twin A):

before throwing the pack: $p_i=(m+M)v_i=0$
after: $p_f=Mv+mu$
... if m is the mass of the pack and M is the mass of Alice, u and v are the respective velocities. Since pf=pi you can find relationships between the masses and the speeds.

Bob gets an incoming pack mass m moving at speed u.
You should be able to do the rest.