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Sagot :
Given
A rectangular painting is 120 cm wide and 80 cm high.
To find
At what speed must the painting move parallel to its width if it is to appear to be square?
Explanation
According to length contraction, the proper length of an object contracts when it moves with a velocity.
Thus,
[tex]\begin{gathered} l=l_o\sqrt{1-\frac{v^2}{c^2}} \\ \Rightarrow80=120\sqrt{1-\frac{v^2}{c^2}} \\ \Rightarrow\frac{2}{3}=\sqrt{1-\frac{v^2}{c^2}} \\ \Rightarrow\frac{4}{9}=1-\frac{v^2}{c^2} \\ \Rightarrow\frac{v^2}{c^2}=1-\frac{4}{9} \\ \Rightarrow\frac{v^2}{c^2}=\frac{5}{9} \\ \Rightarrow v=\frac{\sqrt{5}}{3}c \end{gathered}[/tex]Conclusion:
The required velocity is
[tex]\frac{\sqrt{5}c}{3}\frac{m}{s}[/tex]
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