Example

The UNC ram of mass 100 kg is carried by some naughty (but intellectually curious) Duke students up in an airplane to a height of 5000 m and thrown out. On the ground below a student armed with a radar gun measures and records the velocity of the ram as it plummets toward the hard, hard ground. Assuming that the fluffy ram experiences a drag force on the way down of $-bv$ with $b = 10 kg/sec$: a) describe qualitatively the measurements recorded by the student; b) how fast is the fat, furry creature going when it splats all over the pavement.

The student sees an exponential approach to terminal velocity:

$$v(t) = \frac{mg}{b}\left(1 - e^{-\frac{b}{m}t}\right)$$ (2.71)

with $v_t = v(\infty) = \frac{mg}{b}$. This fall is far enough to ``reach'' $v_t = 100$ m/sec, since it takes many times $\frac{m}{b} = 10$ seconds to fall 5000 m.