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asleight
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Homework Statement
Given that a puck's velocity is speed [tex]v[/tex] at an angle [tex]\theta[/tex] (measured in radians) with the x-axis, we know that the puck's x-velocity is [tex]v\cos(\theta)[/tex]. Given the error in [tex]v[/tex] is [tex]\sigma_v[/tex] and the error in [tex]\theta[/tex] is [tex]\sigma_\theta[/tex], what is the resulting error in the puck's x-velocity?
The Attempt at a Solution
Solving for partials, we get:
[tex]\sigma_{v_{x}}=\sqrt{\left(\cos(\theta)\sigma_{v}\right)^2+\left(-v\sin(\theta)\sigma_{\theta}\right)^2}[/tex].
Or, using proportionalities of errors, we find:
[tex]\sigma_{v_{x}}=\sqrt{\left(\frac{\sigma_{v}}{v}\right)^2{v_{x}}^2+\left(\frac{\sigma_{\theta}}{\theta}\right)^2{v_{x}}^2}[/tex].
These yield two different values... Which is a real propagation?