Conservation of Mechanical Energy OpenGL/C++ program

i have a small project that i need to finish and im not understanding the math of how to make this work right. I have screen shots of the instructions provided (some info in the instructions was inserted pictures so it wouldnt copy/paste right, hence the screen shots) along with the zip file of headers, source code and such that was provided. In the [login to view URL] file is a spot where the new code is to be put and thats it. math and small amount of code based off that math to get it working right. create an OpenGL/C++ application that will simulate a ball rolling in a valley or half pipe. Students will be given a terrain class that has a sample surface created and methods to get the height at any point. Students will create a simulation where the user will use the left-right arrow keys to change the ball’s horizontal velocity. The application will update the ball’s position on the terrain and the velocity based on conservation of mechanical energy rather than Newton’s second law. $20 budget as its not much to do, just something I'm not understanding.