Horizontal projectile motion: comparing free fall and drag resistance

The motion of a particle that is projected into a resistant medium and subjected to a uniform gravitational field is considered. The drag force that acts upon the particle within the medium is proportional to the particle’s speed, the density of the medium, and the cross-section area of the projectile. We review the problem of a horizontal motion with a drag force that is linear in speed. The problem is formulated in terms of particle speed, mass, height, time, and expelled gas velocity. The equations of motion are solved analytically, and a case study is discussed. As a result, we obtain the deviation of the projectile as a function of time because of the expelled gases with or without drag force.