One Dimensional Hot Air Balloon Kinematics

  • Thread starter Flippit
  • Start date
  • #1
9
0

Homework Statement


A hot-air balloon has just lifted off and is rising at the constant rate of 2.3 m/s. Suddenly one of the passengers realizes she has left her camera on the ground. A friend picks it up and tosses it straight upward with an initial speed of 12 m/s. If the passenger is 2.5m above her friend when the camera is tossed, how high is she when the camera reaches her?


Homework Equations



One-Dimensional Kinematics


The Attempt at a Solution



First I tried setting the distances of the balloon and the camera equal to each other,

camera: 12t+.5*-9.81t^2
balloon: 2.3t+2.5

12t+.5*-9.81t^2=2.3t+2.5

then I rearranged the equation

12t-4.905t^2-2.3t=2.5
9.7t-4.905t^2-2.5=0
-4.905t^2+9.7t-2.5=0

Next, I plugged the equation into the quadratic formula.

t= -9.7+-sqrt 9.7^2-4.905*-2.5/2*-4.905
t= -9.7+-sqrt 94.09+19.62*-2.5/-9.81
t= -9.7+-sqrt 94.09-49.05/-9.81
t= -9.7+-sqrt 45.04/9.81
t= -9.7+-6.71/9.81
t= .305, 1.67

next, I plugged the t value into the formula x= Xi + Vi*t + .5at^2
x= 0 + 12*.305 + .5*-9.81*.305^2
x= 3.66-4.905*.093
x= 3.66 -.456
x= 3.2m

I entered this into the website we turn our homework into, but it said the answer was incorrect, I'm not really sure what I did wrong, all my math seems correct.
 
Last edited:

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
251
Welcome to PF!

Hi Flippit! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)
x= 3.2m

I entered this into the website we turn our homework into, but it said the answer was incorrect, I'm not really sure what I did wrong, all my math seems correct.

Looks ok to me. :confused:

(except I would have used the 2.3t+2.5 equation at the end, instead of the quadratic :wink:)
 
  • #3
9
0
Alright, I guess I'll just have to talk to my teacher about it. Thanks for looking it over!
 

Related Threads on One Dimensional Hot Air Balloon Kinematics

Replies
4
Views
3K
Replies
5
Views
6K
Replies
1
Views
2K
Replies
2
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
6
Views
6K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
13
Views
6K
Top