Height equation in a weird way.

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SUMMARY

The discussion revolves around calculating the height of a hot air balloon using the altimeter's faulty reading, represented as A*h, where A is an unknown constant. The balloonist can drop two rocks and measure the time it takes for the echoes to return, using the equations of motion: y = y0 + V0T + 0.5GT^2, with G set to -9.81 m/s². The proposed solution involves calculating the difference in heights from the two drops, leading to the conclusion that the multiplication factor A can be determined by the ratio of the altimeter readings to the calculated height difference (Dhr).

PREREQUISITES
  • Understanding of kinematic equations, specifically y = y0 + V0T + 0.5GT^2
  • Knowledge of gravitational acceleration, G = -9.81 m/s²
  • Familiarity with the concept of echoes and sound travel time
  • Basic algebra for manipulating equations and solving for variables
NEXT STEPS
  • Study the principles of kinematics in physics, focusing on free fall and projectile motion
  • Learn about the speed of sound in different mediums and its relevance in echo calculations
  • Explore the concept of calibration in measurement tools, particularly altimeters
  • Investigate methods for error analysis in experimental physics
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Students in physics, particularly those studying mechanics, as well as educators looking for practical applications of kinematic equations in real-world scenarios.

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Homework Statement



A hot air balloonist forgot to calibrate his altimeter before taking off. The altimeter displays his height as A*h (A being a constant multiplcator, and h is his real height). He does not know A, nor does he know the speed of sound. How can he find his height with just two rocks that he can drop over a canyon and listen for their echoes. Neglect air resistance.


Homework Equations


y=y0+V0T+.5GT^2
G=-9.81

The Attempt at a Solution


I assumed V0 and Y0 is equal to 0.
Dt (difference in time) is equal to T2-T1
I disregarded the speed of sound because it is a constant in both drops.

First drop:
y1=-4.905(T1)^2
Second drop:
y2=-4.905(T2)^2

(Dhr)(difference in real heights) is y2-y1=

-4.905(T2)^2+4.905(T1)^2

If I record the heights the altimeter gives me at the two points, and find the difference and then divide that by my (Dhr), I should get my multiplication factor right? That is assuming the equation for the (Dhr) is right.
 
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The question doesn't ask you to find A so you figured out the problem already
 
So I my equation for A (the multiplaction factor) is correct? It was right of me to disregard the speed of sound?
 

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