When Should Air Resistance Be Considered in Free-Fall Calculations?

[hainam0101]

Homework Statement

When we solve free-fall problems near Earth, it's important to remember that air resistance may play a significant role. If its effects are significant, we may get answers that are wrong by orders of magnitude if we ignore it. How can we tell when it is valid to ignore the effects of air resistance? One way is to realize that air resistance increases with increasing speed. Thus, as an object falls and its speed increases, its downward acceleration decreases. Under these circumstances, the object's speed will approach a limit, a value called its terminal speed. This terminal speed depends upon such things as the mass and cross-sectional area of the body. Upon reaching its terminal speed, its acceleration is zero. For a "typical" skydiver falling through the air, a typical terminal speed is about 51.6 m/s (roughly 116 mph). At half its terminal speed, the skydiver's acceleration will be about 3/4 g. Let us take half the terminal speed as a reasonable "upper bound" beyond which we should not use our constant acceleration free-fall relationships.

(a) Assuming the skydiver started from rest, estimate how far, and for how long, the skydiver falls before we can no longer neglect air resistance.

Homework Equations

v2=v1 + a*(delta)t

The Attempt at a Solution

Still trying.

 

[Delphi51]

Your v2 equation looks great! Use it to find out when the velocity reaches 51.6/2.

It might be possible to get a more accurate answer by guessing how the acceleration changes, possibly saying a = 9.81 - kt and finding what value of k gives you that 3/4g value. But I doubt if you are expected to get into this "2nd order approximation" business.

 

[hainam0101]

the acceleration is decreasing. so what a value should i use to apply into that v2 equation.

 

[Delphi51]

I would just use 9.81.
I mentioned how you would go about making a better estimate, but doubt if you are expected to do that.