It seems like you understand the basic situation of the problem. In order to find the net force, you need the acceleration of the kayak.
I hope you realize why you cannot do this. In case you don't, you are trying to divide velocity by distance: this does not give you acceleration (you can...
Elastic does mean that the balls don't stick, however your analysis presupposes that the masses are identical. If they are not identical, then p1' is not zero. In fact, just by looking at the speeds given, you should be able to determine that m1 is a bit more massive than m2 (before you double...
The problem provides the initial speed of ball 1 and the final speed of ball 2, you should be able to use those numbers to find the ratio of the ball's masses m2/m1. Once you find this quantity, you have enough information to determine the final speed of ball 2 if m1 doubles.
Hint: Solve for...
You may want to consider some of the basic properties of these quantum states. For example, what must the value of <\mu_1|\hat L|\mu_1> be? What about <\mu_0|\hat L|\mu_1>? Is it possible to calculate the energy of the angular momentum states: <\mu_1|\hat H|\mu_1>?