A 0.500-kg sphere moving with a velocity (2.00i ─ 3.00j + 1.00k) m/s strikes another sphere of mass 1.50 kg moving with a velocity (─1.00i + 2.00j ─ 3.00k) m/s.
(a) If the velocity of the 0.500-kg sphere after the collision is (─1.00i + 3.00j ─ 8.00k) m/s, find the final velocity of the 1.50-kg sphere and identify the kind of collision (elastic, inelastic, or perfectly inelastic).
(b) If the velocity of the 0.500-kg sphere after the collision is (─0.250i + 0.750j ─2.00k)/s, find the final velocity of the 1.50-kg sphere and identify the kind of collision.
(c) What If? If the velocity of the 0.500-kg sphere after the collision is (─1.00i + 3.00j + ak) m/s, find the value of a and the velocity of the 1.50-kg sphere after an elastic collision.