Question

Newton second law - Diff Eq problem

Answer 1

A 9kg object falls vertically downward. The magnitude of the force of air resistance is given by R = 6|v|. Take positive to be downward, Let y(0)= 0, v(0)=0, and let g = 10m/s^2

Answer 2

a. Write a differential equation for the velocity of the object and solve. b. What is the limiting velocity of this object. c. How far has the objecgt fallen when it reaches
80% of the limiting velocity

Answer 3

so far i know that ma = W - R W = weight and R being the air resistance

Answer 4

which basically might as well equal m(dv/dt) = mg-bv => dv/dt = g - (b/m)v

Answer 5

Do you know how to solve non-homogenous, first order, ODEs?

Answer 6

Nope, I haven't been taught how to "solve" any ODE yet

Answer 7

i know how to separate homogenous equations and then do IVP but that's about it

Answer 8

You have:
\[\frac{dv}{dt}=g-\frac{b}{m}v \implies \frac{dv}{dt}=-\frac{b}{m}(v-\frac{gm}{b})\]
\[\frac{dv}{v-\frac{mg}{b}}=-\frac{b}{m}dt \implies \ln \left| v-\frac{mg}{b} \right|=-\frac{b}{m}t+C\]

Answer 9

Yeah, here's what I don't understand. How does g - bv/m = -b/m(v-gm/b)

Obviously she's factoring out a -b/m but where does that come from

Answer 10

Its just to make it simpler to integrate.

Answer 11

Ohhhhh, no i totally see what's going on now