I am a formal instructor and one of the classes I teach revolves(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Max Height and Time

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