A smooth sphere with radius r is anchored on a horizontal plane, and its apex is denoted as point P. An object is projected horizontally from point P with an initial velocity ??0. (a) Determine the minimum initial velocity ??0 required for the object to reach the horizontal plane without making contact with the sphere's surface after being projected. (b) If the object freely slides from point P down to the horizontal plane, calculate the height above the horizontal plane at which it departs from the sphere.

1. A smooth sphere with radius r is anchored on a horizontal plane, and its apex is denoted as point P. An object is projected horizontally from point P with an initial FN velocity vo. (a) Determine the minimum initial velocity vo required for the object to reach the horizontal plane without making contact with the sphere's surface after being projected. (b) If the object freely slides from point P down to the horizontal plane, calculate the height above the horizontal plane at which it departs from the sphere