A ball of mass m is released from rest at x=0. Air resistance is expressed as R = kv(adsbygoogle = window.adsbygoogle || []).push({}); ^{2}, where k is a positive constant and v denotes velocity.

Derive an expression for the speed in terms of the distance x that it has fallen.

Identify the terminal v.

I know I have to start with ma = mg - kv^{2}and integrate but I can't seem to separate the variables right to get it as function of x or distance (even though the problem has a picture of a vertical fall)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Free fall w/ Air Resistance

**Physics Forums | Science Articles, Homework Help, Discussion**