alex edited untitled.tex  about 8 years ago

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&= 152.8 \pm 0.3 \text{cm}  \end{align*}  }  \item{Multiply values to find distance, add distance. Again, by assuming that errors are distributed normally, we will take the square-root of the sum of the squared  relative uncertainties, uncertainties. We then  multiply the  relative uncertainty by distance to get absolute uncertainty. \begin{align*}  \text{Distance} &= v\times t = 50\times1.2 = 60\\  \delta(\text{Distance}) &=D(\frac{\delta v}{v}+\frac{\delta t}{t}) &=D\sqrt{\frac{\delta v^2}{v^2}+\frac{\delta t^2}{t^2}}  = D(\frac{3}{50}+\frac{0.1}{1.2})\\ D\sqrt{\frac{3^2}{50^2}+\frac{0.1^2}{1.2^2}}\\  &= 60(\frac{3.6+5}{60})= 8.6\\ 60\sqrt{\frac{12.96+25}{3600}}= 6.16\\  \text{Therefore, Distance} &= 60\pm9 60\pm6  \text{km} \end{align*}  }  \item{There are a few steps to this.