1. The problem statement, all variables and given/known data Hi, I have to model the velocity and displacement of different paper shapes assuming that air resistance, R is proportional to velocity, v. I have also conducted an experiment, and the equation of the line h = 1.532t - 0.366 Where h is the height the paper shape was dropped from, if t is the time taken for it to reach the ground. Model: R = kv Assuming that the only forces acting on the cup are it's mg downwards and R upwards. And that the motion is vertical only. when t=0, v=0 and x=0 I have found the equations for v and x in terms of t. The problem I have is finding k. k= constant in the the assumption R is prop to v. mg= weight of paper cup R= air resistance dv/dt = acceleration x= displacement v= velocity of the paper cup Downwards is taken as positive. I will go through what I have so you know what I am working with and the nature of the problem, but ultimately the problem I have with is k. 2. Relevant equations N[II] gives : m(dv/dt) = mg -kv (dv/dt) + (k/m)*v = g Using an integrating factor: I = e^(kt/m) So d(v*e^[kt/m])/dt = ∫ge^(kt/m)dt Finishing this and using the initial conditions: v = [mg/k]*(1-e^[-kt/m]) Integrating this we get displacement: x = [mg/k]*(t+(m/k)e^(-kt/m)+c) Using initial conditions: x= [mg/k]*(t+(m/k)*[e^(-kt/m)-1]) 3. The attempt at a solution I know that t -> ∞ v-> mg/k [which will be an asymptote when plotted] So the terminal velocity = mg/k I also know that the x against t graph will look like a curve with an increasing gradient, until the time at which the terminal velocity is reached. At this time the gradient will become constant. Ok so now we find k--- how? Thanks in advance.