In this article, we apply the well-known equations of projectile motion to the case of a fighter pilot ejecting from an aircraft, the aim being to establish under what conditions there is danger of impact with the rear vertical stabilizer. The drag force on the pilot after ejection is assumed to vary as the velocity squared and the aircraft motion is assumed to be confined to a plane (i.e. roll, yaw and pitch are not included), but it is not restricted to horizontal flight. The study is, however, limited to the case of no propulsion force acting on the pilot after ejection, as is appropriate to the older style of ejection seat. The problem has been coded in MATLAB and some illustrative numerical results are presented. We envisage that student interest in the numerical solution of differential equations will be stimulated by this application of projectile motion to an interesting real-life and potentially life-threatening situation.