• Support PF! Buy your school textbooks, materials and every day products Here!

1-d kinematic problem

  • Thread starter captain
  • Start date
  • #1
163
0

Homework Statement


A canonball is launched up in the air with velocity v_0. There is air resistance, which is equal to kmv (where k is some proportionality constant and m is the mass of the canonball) and is proportional to the canonball's velocity. How long does it take to reach its maximum height.


Homework Equations





The Attempt at a Solution



I got t=ln(g)/k as the time. I would just like to verify if that is the correct solution. g=earth's gravitational acceleration constant.
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,622
6
Your answer is incorrect. Perhaps if you showed your working we could point you in the right direction...
 
  • #3
163
0
Your answer is incorrect. Perhaps if you showed your working we could point you in the right direction...
i realize that my units are off by a lot. i realized that i get the total acceleration to be
-kv+g=(dv)/(dt), but when i try and integrate it by (dv)/(-kv+g)=dt i get incorrect units. is the g supposed to stay on the other side of the equation. If so how can I integrate it? and after that I am not quite sure about how to use v_0 given to me?
 
  • #4
163
0
i would like to verify if this is correct. I checked to make sure if it is in the right units.

t=-ln[(v_0/g)k +1]/k
 
  • #5
learningphysics
Homework Helper
4,099
5
i would like to verify if this is correct. I checked to make sure if it is in the right units.

t=-ln[(v_0/g)k +1]/k
I'm getting exactly the same thing but without the minus sign.

I think the minus sign shouldn't be there because ln(positivenumber + 1) > 0... so with that minus sign there you'll get a negative time.
 
  • #6
163
0
i got it in terms of my integration bounds for the integral with dv. i set the bounds from v to 0
 
  • #7
learningphysics
Homework Helper
4,099
5
-kv+g=(dv)/(dt),
should you be using -kv - g... or are you using g = -9.8 instead of g = 9.8?
 
  • #8
163
0
i see i was doing it wrong the whole time
 
  • #9
163
0
i accidentally made the force in my free body diagram like this:

m(-a)=-f_drag-mg

i thought that since the acceleration was negative with respect to my reference frame, the -a was necessary when the right hand side of the equation took care of that.
thanks for your help.
 

Related Threads on 1-d kinematic problem

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
11
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
11
Views
2K
Top