Calculating Displacement in Elastic Collision of Pool and Croquet Balls

[Tabe]

I swear, this is the last problem that I have.
Here it goes...
A pool ball having a mass of .65 kg experiences an elastic collision with a croquet ball having a mass of 1.38 kg. The pool ball had been rolling for 4.3 seconds, having covered a distance of 22.6 meters during that time. The croquet ball had been struck by a mallet only .80 seconds before the collision, and was given an acceleration of 12.6 m/s^2. How far from the point of impact will the pool ball be 1.9 seconds after the collision?

I'm lost on how to start the problem. I am sort of confused on how to solve for the displacement when not given the velocity/acceleration of both objects. I know that there's a way to get around that, but I can't see it. Can someone point out a formula that would help me solve this freakishly annoying problem.

 

[beth314159]

Ill posed

Among other things, the problem as stated does not provide enough information to establish the velocity of the croquet ball. We are told the force (acceleration) impressed, but not the duration of the force (.8 s is the delay between the strike and the future collision with the pool ball).

The velocity of the pool ball can be established from the given information only if we assume rolling with no friction.

-Beth

 

[Tabe]

To find the velocity of the croquet ball, is that even possible, without the time? Could I use the .80 seconds as a point in time and base my info off of the collision?

 

[Tabe]

I solved for the final velocity, and I got 10.51m/s. Then I used the conservation of momentum equation, and for the velocity of the croquet ball, I got 4.95m/s. So, to find the distance from the collision point, would I just use this kinematics equation, x=1/2Vft?

The answer that I got is 4.7025 meters. Is that close to being right?