Box on top of a plane!

Classical Mechanics Level 3

A block of mass \(5 \text{kg}\) is placed on top of an aeroplane moving horizontally with an acceleration of \(11 {\text{m/s}}^2\) at a height of \(500 \text{m}\) above the ground. If the box is placed at a distance of \(10 \text{m}\) from the tail of the aeroplane, then calculate the total time taken by the block to reach the ground.

Details and assumptions:-

  • Assume that the air resistance is negligible.
  • Assume that the aeroplane is of negligible width and does not change its direction during flight.
  • Assume that the box does not collide with the tail of the aeroplane just before falling off the aeroplane.
  • Take \({\mu}_{\text{s}}\) (co-efficient of static friction) between the block and the aeroplane's surface as \(0.5\).
  • Take \(\text{g}\) (acceleration due to gravity) as \(10 {\text{m/s}}^2\).
  • Give your answer (in seconds) correct to two decimal places.

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