I am a formal instructor and one of the classes I teach revolves around the ballistics of a bullet. I am currently in a Calculus class and will be starting as an Economics major In the fall when I finish my time in the Marines. I am hoping to see if there is any way, through calculus that I can prove the max height of the round through actual mathematical proof. Many of the lesson plans and outlines simply indentify what I have attached below and do not mention proof of this. I am simply curious if I can prove the max height of the round and at what time during its flight path does it reach this height. Any help would be greatly appreciated. Below is a simple diagram of a rifle trajectory at 300 yards. I attached the image to give a preliminary view of what I am referencing. Maximum Ordinate - The highest point in the trajectory of the round on its route to the target The event I would like to know if I can prove is how high the maximum ordinate should be. I am new to calculus and especially the application of calculus to real world events. Can I use a Derivative function formula to find the max? If so, what variables do I need for this, the rounds are all constant, and with that the velocity of the round at specific ranges is also fixed (in theory). Would I use a function like h(t) = 4t^2+48t+3 to find the maximum h and the corresponding time t. The conventional knowledge says that roughly 2/3rds of the way to the target the projectile reaches its maximum height. It is said to be roughly 7 inches above the line of sight at its highest moment, which is supposedly 2/3rd of the way to 300 yards. This is what I am trying to prove or disprove throughcalculus. All in all, any help or nudges to this type of problem would be greatly appreciated.