Horizontal pinball

Classical Mechanics Level 3

A ball of mass \(2 \text{kg}\) is placed in front of a spring having a constant of \(20 \text{N/m}\) 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 metres) of the ball when it hits the ground.

Details and assumptions

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

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