Jealous of a Prussian lab's work concerning \(\text{ time dilation }\) an Irish-Sephardic consortium jointly publishes their findings into \(\text{ length contraction }\)of alloy rods. Using the formula: \[ L_{obs} = L \sqrt{1 - \frac{v^2}{c^2}} \] determine the contracted length observed (\(L_{obs}\)) by the consortium when a copper-tin rod of uncontracted length (\(L\)) of \(67 \text{ inches }\) was accelerated to a velocity (\(v\)) of \(0.50c\).

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