Students consider projectile motion of an object that experiences drag force that in linear with the velocity. Students consider the horizontal motion and the vertical motion separately. Students solve Newton's 2nd law as a differential equation.

Consider two particles of equal mass \(m\). The forces on the
particles are \(\vec F_1=0\) and \(\vec F_2=F_0\hat{x}\). If the
particles are initially at rest at the origin, find the position,
velocity, and acceleration of the center of mass as functions of
time. Solve this problem in two ways, with or without theorems
about the center of mass motion. Write a short description
comparing the two solutions.