How Long Before a Dropped Compass Hits the Ground from a Rising Balloon?

In summary, after the balloonist drops the compass over the side of the balloon, it takes 1.23 seconds for the compass to hit the ground.
  • #1
gmunoz18
29
0
Ive been stressing on this problem for a while ill show you the work below

A hot-air balloon is rising upward with a constant speed of 2.60 m/s. When the balloon is 3.20 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?

so first i did the time it took for the balloon to reach 3.2 meters which was 3.2/2.6= 1.23 seconds

and than i did the falling object which i got .808 seconds. using -9.8 as acceleration and found used the basic kinematic equations to get the .808 seconds


i added these together for the round trip to hit the ground and got 2.0389 seconds but this number is not right i don't know what I am doing wrong. I've tried just the regular fall from the balloon and it didnt work. I am lost confused why it isn't working and frustrated thanks a lot in advance
 
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  • #2
Remember the compass, when dropped, had an initial upward velocity, it didnt drop from rest. Did you take that into account?
 
  • #3
no i did not I am going to try and work that right now
 
  • #4
If you don't get it, I think my answer came out to be t=1.11586 seconds from the time the compass is let go till it hits the ground, so that plus whatever time to get the balloon into the air.

using
Xf-Xi = Vi*t + (1/2) a t^2

Solving for t
 
  • #5
gmunoz18 said:
no i did not I am going to try and work that right now

You have the altitude h and the initial speed V_0, so you may apply
V=V_0-gt_1,
and
V^2=V_0^2-2.g.h_1,
and set V=0 to know the time t_1 and the height h_1 that the compass rise further (up to the max height under the action of gravity). That is,
t_1=V_0/g, and h_1=(V_0)^2/(2g).
So by applying now free fall you have
h_1+h=1/2.g.(t_2)^2 (recall that V=0 there, at the max height)
Solve for t_2 and the answer is
t=t_1+t_2.
That is an instructive way to solve it because you know what are doing.
 

Related to How Long Before a Dropped Compass Hits the Ground from a Rising Balloon?

What is Basic Kinematics Balloon?

Basic Kinematics Balloon is a scientific experiment that involves studying the motion of a balloon in various situations to understand the principles of kinematics.

How is Basic Kinematics Balloon set up?

To set up Basic Kinematics Balloon, a balloon is filled with helium gas and tied to a string. The string is then attached to a stand which can be moved to change the direction of the balloon's motion.

What factors affect the motion of the balloon in Basic Kinematics Balloon?

The motion of the balloon in Basic Kinematics Balloon is affected by various factors such as the force of gravity, air resistance, and the direction and magnitude of the string's tension.

What can we learn from Basic Kinematics Balloon?

Basic Kinematics Balloon allows us to understand the concepts of displacement, velocity, and acceleration in a hands-on and visual way. It also helps us understand the effects of different forces on an object's motion.

How can Basic Kinematics Balloon be used in real-life situations?

Basic Kinematics Balloon can be used to study the motion of objects in different environments, such as the movement of a parachute or a skydiver. It can also be used to understand the motion of projectiles or the behavior of gases in a closed container.

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