Answered

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A rectangular painting is 120 cm wide and 80 cm high. At what speed must the painting move parallel to its width if it is to appear to be square?

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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