DE physics problem

Hi /sci/, I have a differential equation question for you.. math stuff.. someone please give me a hint and help me out this is bugging the crap out of me.

Sorry for the HW question, but this is purely to help me understand this... the book doesn't explain the direct connection between the limiting velocity and air resistance.

5. A body of mass 100g is dropped from rest toward the earth from a height of 1000m. As it falls, air resistance acts upon it, and this resistance (in newtons) is proportional to the velocity v (in meters per second). Suppose the limiting velocity is 245m/s.
a. Find the velocity and disnce fallen at time t secs.
b. Find the time at which the velocity is one-fifth of the limiting velocity.

Answers:

a. v=245[1-e^(-t/25)] , x=245[t+25(e^(-t/25)-1)]
b. t=5.58

I set up my equation as

100dv/dt = 981 - kv

Differentiated by seperation,

981-kv=e^(kt)*e^(kC1) , used the initial value v(0)=0
C1=ln(981)/k

Plugged that back in...

v=(981/k)*[1-e^(kt)]

How do I get from here to the first answer?? I don't get how the limiting velocity relates to my v equation.. I think it's the same thing as the limit of v as it approaches infinity, but that makes my equation make no sense. Someone please help!

.572

phail @ integration?  You almost certainly neglected a negative sign and the factor of 100 somewhere.

I got
981 - kv = C₂e^-kt/100
where C₂ is a function of C₁.

>>3
Thanks for the helpful post.. I rechecked my work and realized I was doing sloppy integration as you suggested. Thanks for the pointer.

However, I am still confused by the concept of k. Usually these problems give air resistance as a concrete numeric variation instead of just leaving us to figure it out.

So I got to the point you did and I'm trying to progress further.

I solved for V. This gives:

V=[C3*e^(-kt/100)+981]/k

Should I solve for C and then K? I think that sounds right.

How do you have the nice looking mathematical font? I tried to use the one from word, but that didn't work.

Okay, Op here again.

I keep getting C to be 981 and this makes k=0. Is this nonsensical? I need a little more help please.

Op here again, fuck I'm feeling dumb tonight. The one e side of the equation approaches zero not one... that makes k=4.004 abouts and that makes everything fall together nicely. Yay!

Thanks for the help /sci/ I don't feel like I'm going insane anymore. Can anyone tell me how to have the nice math font so I can write it an a easier to read fashion on this board?

subscript tag: x[sub]1[/sub] produces x₁
superscript tag: x[sup]2[/sup] produces x²

1. Use the [sup] and [sub] tags to enable superscripts and subscripts on lines of equations.

2. Open the faggoty Windows "Character Map" application and find the symbols you need from your default character sets.  Cut-n-paste these into the 4chan message field.

3. Find other free (Unicode) fonts that are designed to deliver math symbols.

4. Learn to use the [code] tag in 4chan.  Ref. BBCode.

Here, I made a simple integral from characters found in the "Lucida Console" font:

⌠π
│ x²dx
⌡0

Ouch.  Some fail there, but not too much.

>>9
but not too much.
Compared to your other posts, yep.
Not too much.

>>10
I just drew an equation.

You just draw scorn.

Do better or GTFO, fagbird.

>>11
Do better or GTFO
That's not much of a challenge.

>>12
You see?  That's why you draw scorn.  When challenged to do better, you don't even SEE IT as a challenge.  Hence, your life is fail.  Fix that with a razor.  NAO.

>>13
You don't remember your own posts do you?
Do better or GTFO, fagbird.
Ofcourse, this implies to do "better" than your particular contribution.
By the way, do you know what scorn means?
When challenged to do better, you don't even SEE IT as a challenge.
It was not a challenge, in the particular context you clearly commanded me to do something.
Clearly, you are the illusionary one, since you believe it was a challenge while it was an order.

Yes, like I said, do better or GTFO.  That's a challenge and you're just not rising to it.  So start with the cutting, gayape.  NAO.

lrn2rd the dictionary

>>15
YHL HAND.