When Will the Package Hit the Ground?

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The discussion focuses on a physics problem involving a package dropped from a hot-air balloon ascending at 10 m/s from a height of 84 m. The key equations discussed include Yf = Vot + (1/2)at^2, with known variables such as initial velocity (Vo = 10 m/s) and acceleration due to gravity (a = -9.8 m/s^2). The main challenge is correctly setting up the equation to solve for time as a function of velocity and position. A suggestion is made to use the quadratic equation to find the time it takes for the package to hit the ground. The conversation highlights the importance of algebraic manipulation in solving the problem.
ATranPV
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Homework Statement


A hot-air balloon is ascending at the rate of 10 m/s at a height of 84 m above the ground when a package is dropped.

Find time it took to hit the ground

Find Final velocity

Homework Equations


The Attempt at a Solution



Initially, I am inclined to use the equation Yf = Vot + (1/2)at^2

I know that a=-9.8 m/s^2
Vo = 10m/s
Yf=84m

With four variables and 3 are known, I can find time.

The part I am having trouble with is setting up the equation where time is a function of velocty and position (where as t=something)

Am I even approaching this problem correctly? Any help will be much appreciated.
ATranPV

EDIT: Yes...my algebra sucks...:(
 
Last edited:
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Hint: To solve for t, use the quadratic eaquation.
 

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