A smooth hemisphere, of radius 2a, is placed with its plane face on a horizontal surface. A

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A smooth hemisphere, of radius 2a, is placed with its plane face on a horizontal surface. A particle, of mass 3m, is placed on the highest point of the hemisphere. The particle is then projected horizontally with speed √1/4ga.

a. Find the height of the particle above the horizontal surface when it leaves the surface of the hemisphere.

b. Find the speed of the particle when it strikes the horizontal surface.

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