Given data:
* The length observed by the observer at rest is,
[tex]l_o=6\text{ m}[/tex]* The actual length is,
[tex]l=8\text{ m}[/tex]Solution:
By the law of relativistic length contraction,
[tex]\begin{gathered} l_o=l_{}\sqrt[]{1-\frac{v^2}{c^2}} \\ 6=8\sqrt[]{1-\frac{v^2}{c^2}} \\ \sqrt[]{1-\frac{v^2}{c^2}}=\frac{6}{8} \\ \sqrt[]{1-\frac{v^2}{c^2}}=0.75 \\ 1-\frac{v^2}{c^2}=0.5625 \\ \frac{v^2}{c^2}=1-0.5625 \\ \frac{v^2}{c^2}=0.4375 \end{gathered}[/tex]Thus, the value of the velocity is,
[tex]\begin{gathered} \frac{v}{c}=0.661 \\ v=0.66c \end{gathered}[/tex]where c is the speed of light,
[tex]\begin{gathered} v=0.66\times3\times10^8 \\ v=1.98\times10^8ms^{-1} \end{gathered}[/tex][tex]\text{Thus, the sp}eed\text{ of the limo is 1.98}\times10^8ms^{-1}[/tex]