This doesn't seem like much more than a kinematics problem but it's for an upper division mechanics course so I chose to post it here. Feel free to move to intro if necessary.
The Attempt at a Solution
I focused only on the vertical component to find the speed at point 1:
Now I found the time it takes to get from point 1 to the top of the path:
0 = √(Vy2 -2gh) -gt
t = √(Vy2 -2gh) /g
To get from the top to point 2 would take the same amount of time so the total time to get from point 1 to 2 is 2*√(Vy2 -2gh) /g
Since there's no acceleration in the x direction the distance between the two points is
2Vx*√(Vy2 -2gh) /g
I think this is the correct answer, however I can't get it to match the given solution. Furthermore even if this is correct it seems like it would take a lot of algebra to match the given solution, leading me to believe another approach was taken. Any help?