Equations of Kinematics, including gravity

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A hot-air balloon rises at a constant speed of 2.20 m/s, and a compass is dropped from 3.30 m above the ground. To determine the time it takes for the compass to hit the ground, kinematic equations must be applied, specifically those relating distance, time, and acceleration due to gravity (9.8 m/s²). The problem can be simplified by breaking it into parts, identifying initial position, initial velocity, and constant acceleration. Understanding the integration of velocity and position is crucial for solving this kinematics problem. Proper application of these concepts will yield the time elapsed before the compass reaches the ground.
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Homework Statement


A hot-air balloon is rising upward with a constant speed of 2.20 m/s. When the balloon is 3.30 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?

Homework Equations

The Attempt at a Solution


I just started taking Physics 1111 at college and never having taken physics in high school, I have no idea where to start. I assume you would use the knowledge that an object falls towards Earth at 9.8 m/s^2... I just don't even know what equation of kinematics to plug this information into? Thank you for your help!
 
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Runner1598 said:

Homework Statement


A hot-air balloon is rising upward with a constant speed of 2.20 m/s. When the balloon is 3.30 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?

Homework Equations

The Attempt at a Solution


I just started taking Physics 1111 at college and never having taken physics in high school, I have no idea where to start. I assume you would use the knowledge that an object falls towards Earth at 9.8 m/s^2... I just don't even know what equation of kinematics to plug this information into? Thank you for your help!
You can start by writing the eqs. of kinematics in section 2 of the template. There are only a handful.

You want an equation which relates distance, time, and acceleration.
 
Starting out, you will do yourself a favor by breaking the problem into parts that are easier to visualize and solve. In this case, what is a good first part of the path of the compass?
 
What is the initial position?
What is the initial velocity?
What is the constant acceleration?

Remember that velocity can be described by:
##\int_{t_0}^t a(s) ds +v(t_0)= v(t)##
and position can be described by:
##\int_{t_0}^t v(r) dr +p(t_0)= p(t)##.

Is simple integration part of your toolkit? What are the equations of kinematics?
 

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