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Falling Speeds: Measure Speed with Uncertainty

Estimate timing resolution and propagate small independent uncertainties.

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For average speed v = h/t, first-order independent standard uncertainties give (sigma_v/v)^2 = (sigma_h/h)^2 + (sigma_t/t)^2. This approximation needs small errors; correlation and systematic bias need separate treatment.

Worked example

For h = 1.00 m, t = 0.50 s, sigma_h = 0.03 m and sigma_t = 0.02 s, v = 2 m/s. Relative uncertainty is sqrt(0.03^2 + 0.04^2) = 0.05, so sigma_v = 0.10 m/s.

A timing interval covers 24 frames at 60 frames per second, giving 0.40 seconds. A one-frame timing uncertainty is approximately 0.017 seconds. Measured speed also depends on distance uncertainty.
A timing interval covers 24 frames at 60 frames per second, giving 0.40 seconds. A one-frame timing uncertainty is approximately 0.017 seconds. Measured speed also depends on distance uncertainty.
Question 1 What is the average speed in the example?
Question 2 What is the relative standard uncertainty?
Question 3 What is sigma_v?
Question 4 How long are 24 frame intervals at 60 frames per second?
Question 5 Does this random-uncertainty formula remove a biased distance scale?