How do I calculate the work due to air drag when throwing a ball in the air?

[Eater]

Homework Statement

There isn't really a "problem statement", but more so a conceptual prompt.

Say you throw a ball in the air with some velocity V. The work done due to gravity and drag is Mgh + F_dragd. What I don't know how to do (and there is no additional information, the prompt is very open ended) is how to find that "d", or if that "d" is relevant at all. Perhaps I'm taking the wrong approach to this.

Know that this data needs to be graphed as a function of time through coding, but that part I can do just fine. It's simply the conceptual part of the equation that I'm not getting.

To make it clear, I'm not sure how to find the work due to gravity and drag on a ball thrown into the air with some velocity V.

Homework Equations

F = kv², F = 1/2ρ*V²A

 

[haruspex]

As you can see from your equations, the force is not constant, so it is not just a matter of finding d. The work done against drag is therefore not just the product of the two. Instead, it is the integral of the force with respect to the distance.
You need to write down the differential equation of motion, starting with F_net=ma. At some instant, at speed v upwards, what is the net force?

 

[rcgldr]

There's a solution if the ball is dropped vertically, I'm not sure if this could be used for a ball thrown upwards vertically:

http://en.wikipedia.org/wiki/Free_fall#Uniform_gravitational_field_with_air_resistance

Otherwise, you'll need to use a method like Runge Kutta (RK4) with differential equations to calculate the result.

To keep the sense of the direction of drag force correct, use F = - 1/2 ρ V |V| Cd A .