91影视

Speed of Anna with respect to the stationary observer is,

Thetime interval $t^{\text{'}}$ measured by a moving observer at velocity$v$ is related to the time interval $t$ of two events measured by a stationary observer and the space interval $x$ of the two events measured by the stationary observer as,

$t^{\text{'}}=\frac{t-\frac{v}{c^2}x}{\sqrt{1-\frac{v^2}{c^2}}}$ .....(I)

Here $c$ is the speed of light in vacuum.

(a)

When the clock at the mid-point of the spaceship reads $t=0$,the time at$24\text{鈥尘}$behind the ship also reads$t=0$. The time at the same location at Anna's ship can be obtained from equation (I) as,

$\begin{array}{c}{t}^{\text{'}}=\frac{0鈭�\frac{0.6c}{c^2}(鈭�24\text{鈥尘})}{\sqrt{1鈭�{0.6}^2}}\\ =6脳{10}^{鈭�8}\text{鈥塻}\\ =60\text{鈥塶蝉}\end{array}$

Thus, the clock reads $60\text{鈥塶蝉}$.

(b)

The clock at $x=0$ and $x=鈭�24\text{鈥尘}$ both read $t=0$. Suppose the friend shifts to Anna's ship, and the clock there reads $t^{\text{'}}=60\text{鈥塶蝉}$, which should also be the reading on the clock with Anna as they are synchronized.

Thus, Anna's age jumped forward by $60\text{鈥塶蝉}$.

(c)

The friend is now at $x=24\text{鈥尘}$. The time at the same location at Anna's ship can be obtained from equation (I) as,

$\begin{array}{c}{t}^{\text{'}}=\frac{0鈭�\frac{0.6c}{c^2}(+24\text{鈥尘})}{\sqrt{1鈭�{0.6}^2}}\\ =鈭�6脳{10}^{鈭�8}\text{鈥塻}\\ =鈭�60\text{鈥塶蝉}\end{array}$

Thus the clock reads $鈭�60\text{鈥塶蝉}$, which will also be the jump in Anna's age.

(d)

In the first case, the friend accelerates towards Anna when he jumps ship. Initially, Anna was moving away from him, and after the jump, Anna was at rest with respect to him. So the friend accelerated toward Anna. Here the clock reading jumped up.

In the second case, initially, Anna was moving toward the friend, and after the jump, Anna was at rest with respect to the friend. So the friend accelerated away from Anna. Here the clock reading jumped backward.

Thus, clock readings jump up when the observer accelerates toward it and jumps down when the observer accelerates away from it.