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## Homework Statement

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.

## Homework Equations

kinematics equations

## The Attempt at a Solution

I focused only on the vertical component to find the speed at point 1:

V

^{2=Vy2 -2gh V=√(Vy2 -2gh) 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*√(}V

_{y}

^{2}-2gh) /g

Since there's no acceleration in the x direction the distance between the two points is

2V

_{x}*√(V

_{y}

^{2}-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?