Another Uncertainty with Equations question

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SUMMARY

The discussion centers on calculating the relative uncertainty in determining acceleration due to gravity using the kinematic equation (vf)^2 = (vi)^2 + 2ad. The participant suggests rearranging the equation to solve for acceleration before applying the propagation of error method. It is established that since the initial velocity (vi) is zero, its uncertainty can be considered negligible in this context. The key takeaway is that proper rearrangement of the equation is essential for accurate uncertainty calculations.

PREREQUISITES
  • Understanding of kinematic equations, specifically (vf)^2 = (vi)^2 + 2ad
  • Knowledge of uncertainty propagation techniques
  • Familiarity with basic physics concepts related to motion and acceleration
  • Ability to perform algebraic manipulations to isolate variables
NEXT STEPS
  • Study the principles of uncertainty propagation in experimental physics
  • Learn how to rearrange equations for solving variables in physics
  • Explore examples of kinematic equations applied to real-world scenarios
  • Investigate the effects of negligible quantities in calculations
USEFUL FOR

Students in physics courses, educators teaching kinematics, and anyone interested in understanding the application of uncertainty in experimental measurements.

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Homework Statement



A useful kinematic equation is

(vf)^2 = (vi)^2 + 2ad

You drop a ball (with zero initial velocity) from the top of a building to measure the acceleration due to gravity. If you measure the final velocity to be vf ± ∆vf, and the height of the building to be d ± ∆d, what is the relative uncertainty in your determination of the acceleration?

Homework Equations



Uncertainties equations, propagation of error.

The Attempt at a Solution



This time I'm really not sure. Should I first rearrange the equation to solve for acceleration, and then do my propagation of error? Or do I take it as it is right now?
 
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yes I think you should solve for acceleration, and you just drop vi because its zero and the uncertainty in that is negligible.
 

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