Sliding down a sliding inclined plane

A box of mass \(2\text{ kg}\) slides without friction down an inclined plane of mass \(5\text{ kg}\) that is free to slide horizontally on a frictionless floor. The height of the inclined plane where the box initially stands is \( 5 \) meters, and the inclination of the plane is \( 30^{\circ} \).

What will be the magnitude of the velocity of the box (with respect to the stationary floor) just before it leaves the inclined plane?

Details and Assumptions:

  • Neglect the dimensions of the box.
  • Take the gravitational acceleration as \( g = 9.81\text{ m / s}^2 \).

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