# Drawing direction fields

1. Aug 5, 2008

### XSK

1. The problem statement, all variables and given/known data

(i'm not sure if this is the correct forum please move it if incorrect)
my problem is with generally drawing direction fields - i dont really know what to do. i have notes but i can't make head nor tail of them. this is an example of a question concerning them:

2. Relevant equations

i know that if you stick the requirments into newton's 2nd law adding constant k you get that equation, and i know to find the terminal velocity you integrate and find v, but i dont know how to sketch the direction field.

3. The attempt at a solution

i see that

dv/dt = -g + k/m

but this seems to be independant of both v and t so how do i plot it as a graph?

even if there were a v or t in that equation i still wouldn't be comfortable to draw the direction field because i don't know what to do >_>;

thanks

Last edited: Aug 5, 2008
2. Aug 5, 2008

### foxjwill

Think of direction fields as a $${dy \over dx} = f(x,y)$$. At each point $$(x,y)$$ on the graph, you draw a tic-mark with slope equal to f(x,y). So here, instead of x and y, we have v and t, and f(v,t)=-g+k/m. What's the slope of each tick mark going to be?

3. Aug 8, 2008

### XSK

uhh
i'm not sure....some kind of straight line?

4. Aug 8, 2008

### HallsofIvy

Staff Emeritus
Check the meaning of the word "slope". It is a number not "some kind of line". What does the slope of a line mean?

5. Aug 12, 2008

### XSK

ok i looked up slope and now know it is a number but the answer to this question still eludes me!

i dont know how you'd put the equation on a graph

the notes i have for this involve looking at the independence of say, x of the equation so im rather stumped. also i just suck at graphs...

Last edited: Aug 12, 2008