I need help solving a physics problem regarding momentum

Question

Eugenia and Bor stand at rest on roller blades as shown in the image below. Eugenia then pushes Bor with some constant force. Bor’s mass is 70 kg and Eugenia’s mass is 54 kg.

1)    State the hypothesis you are testing. The hypothesis should be the idea or general equations that are using to make the prediction.

 2 ) Use the hypothesis to predict the ratio of Bor’s and Eugenia’s speeds after Eugenia pushed Bor.

3) Once you have made your prediction, play the video. Use a stopwatch and the position markers in the video to calculate their speeds. What are some sources of uncertainty?

4)    Make a judgment about whether or not your hypothesis can be rejected or if it is supported based on this experiment. Justify your judgment with evidence from this experiment. What assumptions did you make?

Answer 1

1. A fine hypothesis to test here would be that the momentum of an isolated system is conserved. Here the two people Eugenia and Bor constitute the system, and to the extent that the roller blades eliminate friction we may treat the system as isolated (not affected by external forces). Sine the total momentum of this system is zero before the push (both people are at rest with v = 0), conservation says that the total momentum (Bor's plus Eugenia's) will be zero after as well.
2. Note that momentum is a vector quantity. If Bor's momentum to the right after the push is positive, then Eugenia's to the left must be negative. Conservation then gives the following: (70) (0) + (54) (0) = 70 v Bor + 54 v Eugenia. Thus Eugenia will move to the left with a speed equal to 70/54 times Bor's speed to the right, or 1.3 times Bor's speed.
3. You can determine Bor and Eugenia's speeds after the push by observing how far each travels during some specific time interval, using the position scale in the background along with the video timestamp. Be sure to wait until the push is complete (Eugenia no longer touching Bor) before you begin this calculation. Follow a specific point on each person to obtain as accurate location as you can.
4. Your results likely will not give you exactly the 1.3 ratio calculated, but if they are reasonably close (within the uncertainty of your time and position measurements) then they could support your hypothesis that momentum is conserved.