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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