How to calculate the energy lost in a projectile from drag?

[Necm]

The force of drag is proportional to velocity, but with a projectile velocity isn't constant, so how could i calculate the energy lost due to drag?
The projectile in question is being shot straight upwards, so that may make this problem much more simple.

 

[pixel]

Is this an actual experiment, where you will be measuring things like velocity, or is it a theoretical exercise where you will be given values for certain quantities?

 

[russ_watters]

The force of drag is proportional to velocity, but with a projectile velocity isn't constant, so how could i calculate the energy lost due to drag?
The projectile in question is being shot straight upwards, so that may make this problem much more simple.

Well, the energy lost is force times distance and the force of drag is a square function of velocity. You should be able to put that together (with, in this case, gravity) to find the energy loss due to drag.

 

[pixel]

You could use the potential energy difference corresponding to the maximum height you'd expect without drag and the maximum height with drag.

 

[FactChecker]

These problems are usually simulated in small time steps. At each time step, the object velocity and orientation is known and the resultant drag force is calculated. If the object is a sphere, you don't have to worry about its orientation. Otherwise, you need to also calculate aerodynamic rotational forces and keep track at each step of its orientation and resultant coefficient of drag.