Below is a solution to 1-D perfectly elastic collisions by hand:
Note equation 17 is a general solution to all such collisions for and two objects 1 and 2, the final velocity of 1 is given in terms of the initial velocity of each 1 and 2. This expression can be easily rearranged to find, say, the initial velocity of one or the other.
I have written a brief handbook of solved mechanics problems suitable for Physics 220A or 100A.
Some of the problems involve simple calculus, and thus are more suitable for Physics 220A, however
there are many simple problems which would be useful in either course. If interest exists, I will post
figures for some of the problems, which now are figureless.