Answer:
The final momentum of the carts (as a system of two masses isolated) is zero.
Explanation:
The problem states <u>that two carts with the same mass, and the same speed</u> (in magnitude), <u>collide and bounce off of each other elasticaly</u>. As both carts have the same speed magnitude, in order to collide, <u>they have to be advancing from opposite directions</u>, and in the same line, otherwise they couldn't collide at all.
With this conclusion, we can put the analysis in only one dimension, let's say that <em>they are on a x-axis, they have the same mass, and they have opposite velocity with the same magnitude</em>, before they collide.
The momentum can be written in general as
and in our case, n=1, 2.
Then, we calculate the initial momentum in the x-axis, as
Therefore, <em>as the initial momentum is zero, and there are no external forces on the system of two masses (weight and normal cancel each other), and they bounce elastically</em>, then the final momentum is equal to the initial momentum, wich means that
So, the final momentum of the carts (as a system of two masses isolated) is zero (wich is equal to the inital momentum).