# Faster and faster we go

**Classical Mechanics**Level 4

A coin is constrained to move on the surface of a hill and slides from the top of a hill towards the bottom. The height y of the hill as a function of horizontal position is given by \(y=1- \alpha x^2\), where y and x are both measured in meters and \(\alpha=1~m^{-1}\). The coin has a mass of 10 g and is at the top of the hill at t=0 with an initial energy of 0.103 J (where we set the zero of potential energy at y=0). When the coin has reached x=1 m, what is the horizontal component of the coin's velocity **in meters/second**?

**Details and assumptions**

- You may neglect friction and air resistance.
- The acceleration of gravity is \(-9.8~m/s^2\).