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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