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 \(-9.8~m/s^2\).

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