Calculating Air Drag for Projectiles Lab

[bwong]

Homework Statement

I am unable to calculate air drag for a projectiles lab I am doing.
It involves shooting elastic bands and measuring the distance they travel and compare it to the theoretical distance(with and without friction).
It takes 0.45 seconds for the elastic band to fall and its initial velocity is dependent upon the stretch. I also have measured the mass(0.37grams) and the k value (31 N/m).

Homework Equations

the equation 1/2 ACdrag p v^2 is only valid for the initial drag force, but since the projectile loses velocity as time increases, how would i calculate the average drag force. (I also do not know the final velocity)

The Attempt at a Solution

I have thought about integrating the graph Fdrag v.s V, however, I do not have the final velocity.

 

[quantumdude]

The average velocity is easy. It's just the change in position divided by the change in time. You'll need to do this for both the horizontal and vertical components of the motion. You can deduce the final velocity as follows. In Calculus I you would have learned that the average value $f_{av}$ of a function $f$ is given as follows.

$$f_{av}=\frac{1}{b-a}\int_a^bf(x)dx$$

Since you know $f_{av}$, as well as the integrand and the lower limit of integration, you can find the upper limit of integration (which in your case will be the final speed).