Free fall velocity equation?

  • #1
RJLiberator
Gold Member
1,095
63

Homework Statement


I am tasked with coding some graphs regarding free fall motion.

I am unclear what the professor means regarding the following, so I am looking for incite here.

Problem: Solve numerically free fall velocity equation (problem 1.1), compare with exact solution
(1.1) dv/dt = -g

The exact numerical solution and the coding solution should agree here.

My problem is what does dv/dt= -g mean as free fall velocity?

I thought that when you take the derivative of velocity, you get acceleration. That should be what it is saying. (as it is).
She states that she wants us to solve the free fall velocity equation and directs us to dv/dt=-g. Does this make sense?

My understanding is that free fall velocity is v(t) = g*t which is a linear graph


Any clarity on the wording?
note* I can't talk to her as it is due Monday.
 

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,562
5,969
V=-gt would be the exact solution, assuming zero velocity at time 0. A numerical solution would consist of calculating the velocity at a sequence of times using the relationship ##\Delta v=(dv/dt)\Delta t##. You are given what to substitute for dv/dt.
 
  • Like
Likes RJLiberator
  • #3
RJLiberator
Gold Member
1,095
63
Okay, so we both agree that this graph should be linear and that what she is asking for the a velocity graph.
The exact solution I was able to graph and I took into account initial velocity.

one.JPG


So now I have to just add in the numerical solution as you stated.
The numerical solution would then be -g*(change in time)
But this doesn't make sense to me. Because -g*change in time would just be a constant and not a linear down slope.
 
  • #4
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,562
5,969
But this doesn't make sense to me. Because -g*change in time would just be a constant and not a linear down slope.
Change in velocity = -g*change in time . Pick some time interval ##\Delta t=T##.
v0=0;
v1=v0+(-g)T;
etc.
 
  • Like
Likes RJLiberator
  • #5
RJLiberator
Gold Member
1,095
63
Ah, beautiful.

I just want to confirm one thing with you.
The assignment calls for:
–Solve numerically free fall velocity equation (problem 1.1), compare with exact solution
and later states:
Use TGraph to show numerical solution for v(t) and TF1 to illustrate the exact solution (on top of it)

For some reason, she drew a slightly parabolic curve for the 'example graph' in class on the white board.
I don't see how this could, in any sense, be parabolic and I don't understand how any of our current analysis could be skewed.

We seem to be right on with what she has stated as the assignment here and I will use my exact solution (previously pictured) with the numerical approach (as you helped me with here).
And the outcome will be two linear functions essentially graphed right on top of each other.
That seems to clear the assignment, agreed?
 
  • #6
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,562
5,969
she drew a slightly parabolic curve for the 'example graph' in class on the white board.
Since I was not in the class, I cannot say what the drawing meant. Maybe she was illustrating the basic method of plotting a numerical solution, which would in general give some curve.
You did write
The exact numerical solution and the coding solution should agree here.
I was not quite sure what that meant, but I interpreted it as meaning the numerical solution would exactly match the algebraic solution. That would only ever be true for a straight line.
 
  • Like
Likes RJLiberator
  • #7
RJLiberator
Gold Member
1,095
63
Excellent, thank you for your help here!
 

Related Threads on Free fall velocity equation?

  • Last Post
Replies
4
Views
4K
  • Last Post
2
Replies
25
Views
4K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
3
Views
3K
Replies
1
Views
3K
Replies
11
Views
6K
  • Last Post
Replies
6
Views
16K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
2
Views
3K
Top