4. Let's consider two equal point masses (m1 = mg E m) near the surface of the earth and we'll assume air resistance is negligible. m1 is launched into the air from the ground with an initial velocity 170 = voggi + voyj, let's not worry about the actual values of the components. For simplicity, let's place the origin of our coordinate system at the initial location of m1, so its initial position is just zero. m2 is initially a distance are to the right of m1 and a height yo above m1, and dropped from rest the same moment that m1 is launched into the air. 07712 340 721/110 rc $0 a) Find the initial velocity and initial position of the center of mass of the system. b) For now let's assume m1 and m2 do not collide. In this case, we know their positions, velocities, and accelerations at all times. Calculate the center of mass, the velocity of the center of mass, and the acceleration of the center of mass. Wherever possible, express your answer in terms of the initial position / velocity of the center of mass calculated in part a). You should nd that the center of mass acts like an object undergoing projectile motion with the initial position/ velocity calculated in part a). c) Now suppose m1 and m2 undergo a completely inelastic collision when m1 is at its maximum height. This requires 2 _ UOIUOy \" 330 yo: 9 9 Let's just assume the collision happens instantaneously. Make sure you can derive these relationships. Show that after the collision the combined object m1 and m2 has the same position, velocity, and acceleration as the center of mass that you calculated in part b)