Question

Anna and Bob have identical spaceship 60m long. The diagram shows Bob’s observations of Anna’s ship, which passes at a speed of $\mathit{c}\mathbf{/}\sqrt{\mathbf{2}}$. Clocks at the back of both ships read just as they pass. Bob is at the center of his ship and at t = 0 on his wrist watch peers at a second clock on Anna’s ship.

(a) What does this clock read?

(b) Later, the back of Anna’s ship passes Bob. At what time does this occur according to Bob?

(c) What will observers in Bob’s frame see on Anna’s two clocks at this time?

(d) Identify two events that show time dilation and two that show length contraction according to Anna.

Short answer

(a) The value of Anna’s clock read at time$t\mathit{\text{'}}=-100\mathrm{ns}$ .

(b) The value of Bob time occurs later, the back of Anna’s ship passes is $t\mathit{\text{'}}=141\mathrm{ns}$.

(c) The value of position of two clocks according to Bob’s to get the readings on Anna’s frame is $t{\mathit{\text{'}}}_{\mathit{1}}\mathit{\approx }100\mathrm{ns}$and role="math" localid="1659757948068" $t{\text{'}}_2$=0.

(d) It confirms that the events have been time dilated and length contracted from Anna's perspective by using the correct time and length, together with the length contraction and time dilation formulae.

Step-by-step solution

Write the given data from the question.

Consider the Anna and Bob have identical spaceship 60m long.

Consider a speed of ships passes at $c/\sqrt{2}$ .

Consider a time of ship reads at t = 0.