Halliday, Resnick & Walker — Center of Mass and Linear Momentum: Problem 14

14 In Figure 9-33, two particles are launched from the origin of the coordinate system at time t = 0. Particle 1 of mass $m_1 = 5.00 \text{ g}$ is shot directly along the x axis on a frictionless floor, with constant speed 10.0 m/s. Particle 2 of mass $m_2 = 3.00 \text{ g}$ is shot with a velocity of magnitude 20.0 m/s, at an upward angle such that it always stays directly above particle 1. (a) What is the maximum height $H_{max}$ reached by the com of the two-particle system? In unit-vector notation, what are the (b) velocity and (c) acceleration of the com when the com reaches $H_{max}$?