Consider two balls on a horizontal, frictionless surface. Ball A (with mass ma) is moving toward ball B (with mass mb = 1 kg). Ball B is initially at rest. a. (5 pts) If their collision is perfectly elastic, what should be the mass of ball A such that it stops upon collision if ball A's initial velocity is +3.1416 m/s?b. (5 pts) Using conditions in question (a), what is the speed of ball B after collision? Is it moving in the initial direction of ball A or opposite it?c. (5 pts) Consider this 2nd scenario: If the collision is perfectly inelastic, what is the speed of the balls after collision? [Use the mass that you calculated from question (a) for ball A.]d. (5 pts) Now, consider a 3rd scenario: Ball A (with arbitrary speed va) collides with a stationary ball B (mass is mb = 1 kg). After collision, you observed that ball A and ball B are now moving at the same speed va but toward opposite directions: Ball A is heading opposite its original direction, while B is moving along the initial direction of A. What is the mass of ball A?