Classical Dynamics of Particles and Systems · Problem 2-11

Oscillations — Marion & Thornton

Physics — Mechanics · falling-particle-quadratic-resistance

Problem

Consider a particle of mass

m

whose motion starts from rest in a constant gravitational field. If a resisting force proportional to the square of the velocity (i.e.,

kmv^2

) is encountered, show that the distance

s

the particle falls in accelerating from

v_0

v_1

is given by

s(v_0 \to v_1) = \frac{1}{2k}\ln\left[\frac{g - kv_0^2}{g - kv_1^2}\right]