Force vector on falling object to determine terminal velocity and to graph it

[Noise Tank]

Homework Statement

k: constant
v: velocity
m: mass
g: gravity
View attachment qw.pdf

Homework Equations

V_t= √(2mg/CρA)
F=ma

The Attempt at a Solution

part a.

View attachment w.pdf
part b.

View attachment b.pdf
I do not know if i am doing this right and i do not understand how to do part c. If you know how to do this please explain

 

[BruceW]

Welcome to the forum! You've got part (a) correct.

But for part (b), I don't think the equation Vt= √(2mg/CρA) is relevant. You were explicitly given that F_R=-kv, so this is the equation you should be using. In fact, I think you got the answer for (b), before you started using that other equation for the terminal velocity.

Part (c) is a bit trickier. You could either roughly draw what happens, or explicitly calculate the form of the graphs, then draw them.