91影视

The given data can be written as:

• The length of each spaceship is ${\mathrm{x}}^{\text{'}}=100\mathrm{m}$.
• The speed of Anna鈥檚 spaceship is $\mathrm{v}=0.8\mathrm{c}$.

The relative motion between Anna and Bob is used to calculate the position of Bob and reading of the clock by Bob Jr. The formula of time dilation and length contraction is used for the calculation.

$\mathrm{x}={\mathrm{x}}^{\text{'}}\sqrt{1-\frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}$

Substitute all the values in the above equation,

$$\begin{gathered} \mathrm{x}=\left(100\mathrm{m}\right)\left(\sqrt{1-\frac{{\left(0.8\mathrm{c}\right)}^2}{{\mathrm{c}}^2}}\right) \\ \mathrm{x}=60\mathrm{m} \end{gathered}$$

Therefore, Bob Jr is data-custom-editor="chemistry" $60\mathrm{m}$behind his own spaceship.

$t^{\text{'}}=\left(\frac{1}{\sqrt{1-{\displaystyle \frac{{\mathrm{v}}^2}{{\mathrm{c}}^2}}}}\right)\left(-\frac{\mathrm{vx}}{{\mathrm{c}}^2}+\mathrm{t}\right)$

Here, v is the speed of spaceship, c is the speed of light, x is the length of each spaceship.

Substitute all the values in the above equation.

$$\begin{gathered} {\mathrm{t}}^{\text{'}}=\left(\frac{1}{\sqrt{1-{\displaystyle \frac{{\left(0.8\mathrm{c}\right)}^2}{{\mathrm{c}}^2}}}}\right)\left(-\frac{\left(0.8\mathrm{c}\right)\left(60\mathrm{m}\right)}{{\mathrm{c}}^2}+0\right) \\ {\mathrm{t}}^{\text{'}}=\left(1.67\right)\left(-\frac{\left(0.8\mathrm{c}\right)\left(60\mathrm{m}\right)}{\mathrm{c}\left({\displaystyle \frac{3脳{10}^8\mathrm{m}/\mathrm{s}}{\mathrm{c}}}\right)}\right) \\ {\mathrm{t}}^{\text{'}}=267脳{10}^{-9}\mathrm{s} \end{gathered}$$

Therefore, the reading of clock for Bob Jr is $267脳{10}^{-9}\mathrm{s}$.