A stationary ball of radius R is irradiated by aiming parameter

A stationary ball of radius R is irradiated by aiming parameter

A stationary ball of radius R is irradiated by a parallel stream of particles whose radius is r, assuming the collision of a particle and the ball to be elastic, find:
(a) The deflection angle 0 of a particle as a function of its aiming parameter b;
(b) The fraction of particles which after a collision with the ball are scattered into the angular interval between ? and ?4 + d?;
(c) The probability of a particle to be deflected, after a collision with the ball, into the front liemisphere (?

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