Question

A stretch limo of the future is 8.0 meters long, but appears to only be 6.0 meters long to astationary observer when driven at speed close to the speed of light. How fast must the limobe driving?

Answer 1

Given data:

* The length observed by the observer at rest is,

`l_o=6\text{ m}`

* The actual length is,

`l=8\text{ m}`

Solution:

By the law of relativistic length contraction,

`\begin{gathered} l_o=l_{}\sqrt[]{1-(v^2)/(c^2)} \\ 6=8\sqrt[]{1-(v^2)/(c^2)} \\ \sqrt[]{1-(v^2)/(c^2)}=(6)/(8) \\ \sqrt[]{1-(v^2)/(c^2)}=0.75 \\ 1-(v^2)/(c^2)=0.5625 \\ (v^2)/(c^2)=1-0.5625 \\ (v^2)/(c^2)=0.4375 \end{gathered}`

Thus, the value of the velocity is,

`\begin{gathered} (v)/(c)=0.661 \\ v=0.66c \end{gathered}`

where c is the speed of light,

`\begin{gathered} v=0.66*3*10^8 \\ v=1.98*10^8ms^(-1) \end{gathered}`

`\text{Thus, the sp}eed\text{ of the limo is 1.98}*10^8ms^(-1)`