Elastic Collision on a Frictionless Track

[komarxian]

Homework Statement

Consider a frictionless track as shown (I will attach an image in a follow up post). A block of mass M₁= 5.00 kg is released from point A. It makes a head-on elastic collision at B with a block of mass m₂ = 10 kg that is initially at rest. Calculate the maximum height to which m₁ rises after the collision.

Homework Equations

p₁+p₂ = p₁' + p₂'
.5mv²+.5mv²=.5mv²'+.5mv²+

The Attempt at a Solution

Okay, so I tried mixing the Kinetic energy with some momentum equations and also potential energy because KE=-U, but I feel like I probably totally screwed up, and when I tried to use kinematics it didn't work out very well.
The answer I got was 5 meters, but I do not know what the correct answer is. (I will post an image with my work as well, because personally I find it hard to read typed math and prefer pictures, and someone else might too) Thank you so much to anyone who can help!

 

[komarxian]

The top is the image that goes with the problem. Below is my work.

 

[haruspex]

Clearly 5m must be too much.
Looks like you found the collision velocity to be 10m/s, which is right if you are taking g as 10m/s₂.
Couldn't follow your working after that. You need to use conservation of momentum and of energy to find the new velocity of the first mass.
Or, if you have been taught it, you can use "Newton's experimental law" with R=1. This can be derived from those two conservation equations.