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).

 

[rwisz]

I would say that the velocity, v, in this equation is most likely referring to the instantaneous velocity of the ball at a specific time, t. This velocity would change as the ball falls due to the effects of drag force and gravity. Therefore, to accurately plot the position of the ball, you would need to calculate the velocity at each time step, using the equations provided, and then use that velocity to calculate the position of the ball. This would result in a continuous plot of the ball's position as it falls.

In terms of the discrepancy among your classmates, it is possible that some are referring to the velocity at the beginning of the time step (v(t)) and others are referring to the velocity at the end of the time step (v(t+dt)). In either case, both values would be needed to accurately calculate the position of the ball. It is important to clarify this point with your teacher or classmates to ensure everyone is on the same page and using the same definitions in their calculations.