What is the position of a falling ball given drag force and unknown velocity?

[hello337]

Homework Statement

I have to make a plot. This plot must illustrates a position of a ball, which is falling. My problem is that I don't know what v is in this equation.
drag force= -C * ||v(t)|| * v

Homework Equations

To calculate the velocity:
v(t+dt)=v(t)+a(t)*dt
where t is time and dt is Δt

The position:
x(t+dt)=x(t)+v(t)*dt

To find a(t) (the acceleration) I use:
a(t)=F(t)/M

where M is the mass f the ball and F(t):

F(t)=force from gravity + drag force

And drag force is:
drag force= -C * ||v(t)|| * v

The Attempt at a Solution

I have discussed it with some from my class and some say v is v(t-dt) .. other say it is just v(t).

 

[gneill]

Homework Statement

I have to make a plot. This plot must illustrates a position of a ball, which is falling. My problem is that I don't know what v is in this equation.
drag force= -C * ||v(t)|| * v

Welcome to Physics Forums.

That looks like it might be a unit vector in the direction of the velocity. I notice that there's a "-" in front of the constant C. That would make the drag force operate in the opposite direction to the velocity, which is expected.

 

[hello337]

Thank you! So you think that v is v(t) ? :)

 

[gneill]

More likely v = v(t)/|v(t)| , making it a unit vector (magnitude of unity).