Horizontal pinball

A ball of mass \(2 \text{ kg}\) is placed in front of a spring having constant \(20 \text{ N/m}\) and compression \(20 \text{ m}\) at a height of \(100 \text{ m}\) above the ground.

Now, the spring is released, giving the ball a horizontal velocity.

Find the total displacement (in meters) of the ball when it hits the ground.

Details and Assumptions:

  • The ball does not rebound after hitting the ground first.
  • Air friction is negligible.
  • The spring is 100% efficient.
  • Take \(g=10 {\text{ m/s}}^2\) as the acceleration due to gravity.
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