An Open Challenge

Consider the above figure. There is a hollow space in the block \(A\) which is allowed to move only in the vertical direction. The inclination of the wedge \( B\) is \( \theta\), as shown.

What should be the minimum force \(F\) (in \(N\)) to be applied on the wedge in the direction as shown, so that when a man standing in the hallow region throws a ball with initial velocity \(u=50\text{ ms}^{-1} \) vertically, he catches it 8 seconds sooner than if he threw the ball with the same initial velocity standing on the ground.

Details and Assumptions:

  • The mass of the block \(A\) including the mass of the person is \( m=196\text{ kg}\).
  • The mass of the wedge \(B\) is \(M=20\text{ kg}\).
  • Acceleration due to gravity is \(g=10\text{ ms}^{-2}\).
  • The hollow region and the dimensions of the wedge are sufficiently large.
  • There is no friction anywhere in the system.
  • The mass of the ball is to be neglected compared to the mass of the wedge.

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