# A feather and a ball falling with air resistance

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1. Oct 15, 2015

### BSH

1. The problem statement, all variables and given/known data
Suppose you drop a feather and a steel ball of equal masses (0.014 kg) at the same time from a height of 2.2 m and you are told that the feather hits the floor 3.5 s after the steel ball. Estimate the value of the terminal velocity of the feather in air. Then, estimate the feather's drag coefficient.

2. Relevant equations
mg - cv = ma

3. The attempt at a solution
I did the calculus as I've done many times before and got that v=(mg/c)(1-e^(-ct/m)) and the terminal veocity = mg/c. The only other thing I feel I could do is assume the air resistance experienced by the ball is negligible, but I don't know how that helps me if I know so little about the feather.

2. Oct 15, 2015

### BSH

Follow-up: do I have to use conservation of energy?

3. Oct 15, 2015

### Staff: Mentor

I think that you should be able to calculate, or at least estimate c, to get a numerical answer for the terminal velocity of the feather. You know how long the steel ball is in the air (it's safe to assume no air resistance), and you know that the feather takes 3.5 sec. longer.

I haven't worked through this problem, but that's the tack I would take.

4. Oct 17, 2015

### HallsofIvy

Staff Emeritus
With air resistance there is no "conservation if energy".