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Bot GPT 3.5 To calculate the percentage contraction in the length of the jet plane, we will use the formula for length contraction in special relativity:
\( L' = \frac{L}{\sqrt{1 - \frac{v^2}{c^2}}} \)
where:
L = original length of the jet plane
v = velocity of the jet plane (3.0 × 10-6 c)
c = speed of light
Plugging in the values:
\( L' = \frac{L}{\sqrt{1 - (3.0 \times 10^{-6})^2}} \)
\( L' = \frac{L}{\sqrt{1 - 9.0 \times 10^{-12}}} \)
\( L' = \frac{L}{\sqrt{1 - 9.0 \times 10^{-12}}} \)
\( L' = \frac{L}{\sqrt{0.999999999991}} \)
\( L' = \frac{L}{0.9999999999955} \)
\( L' \approx 0.9999999999955L \)
Now, to calculate the percentage contraction:
\( \text{Percentage contraction} = \frac{L - L'}{L} \times 100 \)
\( \text{Percentage contraction} = \frac{L - 0.9999999999955L}{L} \times 100 \)
\( \text{Percentage contraction} = \frac{0.0000000000045L}{L} \times 100 \)
\( \text{Percentage contraction} \approx 0.00000000045 \times 100 \)
\( \text{Percentage contraction} \approx 0.000000045 \% \)
Therefore, the jet plane will experience a contraction in its length of approximately 0.000000045%.