A small particle is given an initial velocity u, tangent to the horizontal smooth hemisphere at a radius R from the vertical centreline, as shown at point A in the following figure. As the particle slides past point B, a distance h below A and a distance r from the vertical centreline, its velocity v makes an angle 0 with the horizontal tangent to the hemisphere through B. Show that, 1 0 = cos 2gh h2 1+ R2

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