91影视

Consider a time difference is$\mathrm{螖迟}=10\text{鈥剆}$.

Consider a speed of the plane is$\mathrm{蠀}=420\frac{\text{m}}{\text{s}}$.

Consider a distance is $\text{4200鈥刴}$.

Write the formula of time difference in the plane鈥檚 clock.

${\mathrm{螖迟}}_0=\mathrm{螖迟}\sqrt{\mathbf{1}鈭�\frac{{\mathrm{蠀}}^2}{{\mathbf{c}}^2}}$ 鈥︹�� (1)

Here, $螖\mathbf{t}$ is time difference, $蠀$ speed of the plane and $\mathbf{c}$ speed of light.

Due to relativistic effects, time relative to an object moves more quickly when it is moving very quickly. The time-dilation equation helps explain this:

$螖t=\frac{螖t_0}{\sqrt{1鈭�\frac{{蠀}^2}{c^2}}}$

Arrive at the following expression for the time difference in the plane's clock using the time-dilation equation:

$\begin{array}{c}螖t=\frac{螖t_0}{\sqrt{1鈭�\frac{{蠀}^2}{c^2}}}\\ 螖t_0=螖t\sqrt{1鈭�\frac{{蠀}^2}{c^2}}\end{array}$

Calculate the time difference in the clock of the aircraft using the formula for${\mathrm{螖迟}}_0$:

Determine the time difference in the plane鈥檚 clock.

Substitute $10$ for$螖t$, $420$ for $蠀$ and $\left(3脳{10}^8\right)$ for $c^2$ into equation (1).

$\begin{array}{c}螖t_0=10\sqrt{1鈭�\frac{{\left(420\right)}^2}{{\left(3脳{10}^8\right)}^2}}\\ =9.8脳{10}^{鈭�12}\\ =9.8\text{鈥刾蝉}\end{array}$

According to the findings, the plane's clock would display the time $\text{9.8鈥刾蝉}$ earlier.