91影视

The given data is written as:

• The speed of railroad flat car is $\mathrm{v}=0.6\mathrm{c}$.
• The time for flashbulb is $\mathrm{t}=100\mathrm{ns}$.
• The difference in time is $鈭�\mathrm{t}=27\mathrm{ns}$.

The duration of the event is based on time dilation, and the length of Anna鈥檚 arm is calculated by length contraction. Anna observes the time dilation in the railroad car.

The duration for the event is calculated as:

$\mathrm{T}=\frac{\mathrm{t}}{\sqrt{1-{\displaystyle \frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}}}$

Substitute all the values in the above equation.

$$\begin{gathered} \mathrm{T}=\frac{100\mathrm{ns}}{\sqrt{1-{\displaystyle \frac{{\left(0.6\mathrm{c}\right)}^2}{{\mathrm{c}}^2}}}} \\ \mathrm{T}=125\mathrm{ns} \end{gathered}$$

Therefore, the event is later than the 100 ns.

The length of Anna鈥檚 arm is given as:

$\mathrm{L}=\frac{{\mathrm{c}}^2}{\mathrm{v}}\left(\left(\mathrm{t}+鈭�\mathrm{t}\right)\left(\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}\right)-\mathrm{t}\right)$

Substitute all the values in the above equation.

$$\begin{gathered} \mathrm{L}=\frac{{\mathrm{c}}^2}{\left(0.6\mathrm{c}\right)}\left(\left(100\mathrm{ns}+27\mathrm{ns}\right)\left(\sqrt{1-\frac{{\left(0.6\mathrm{c}\right)}^2}{{\mathrm{c}}^2}}\right)-100\mathrm{ns}\right) \\ \mathrm{L}=\frac{\mathrm{c}\left({\displaystyle \frac{3脳{10}^8\mathrm{m}/\mathrm{s}}{\mathrm{c}}}\right)}{0.6}\left(\left(100\mathrm{ns}+27\mathrm{ns}\right)\left(0.8\right)-100\mathrm{ns}\right) \\ \mathrm{L}=\frac{3脳{10}^8\mathrm{m}/\mathrm{s}}{0.6}\left(101.6\mathrm{ns}-100\mathrm{ns}\right)\left(\frac{{10}^{-9}\mathrm{s}}{1\mathrm{ns}}\right) \\ \mathrm{L}=0.8\mathrm{m} \end{gathered}$$

Therefore, the length of Anna鈥檚 arm is data-custom-editor="chemistry" $0.8\mathrm{m}$.