Question

Abby leaves Earth on a spaceship traveling at speed v while Bill stays on earth. After time ∆t′ has passed according to Abby’s watch, she sends Bill a signal.

(a) Draw a spacetime diagram labelling Abby, Bill, the signal, and each event.

(b) How much time passes before Abby sends the signal, according to Bill’s reference frame? (Answer in terms of v, c, and ∆t′)

(c) When does Bill receive the signal, according to his wristwatch? (Answer in terms of v, c , and ∆t′)

Answer 1

21 et doul This is the Minkowski diagram on space-time diagram. Here, B = position of Bill - Azposition of Abby. x-et is the frame of reference w..t to Bill. which is fixed at earth x-et is the frame of reference moving with a velocity v where Abby is situated. along AB the signal travels from Abby to Billi,

b) Let according to Bill the time taken is at Now, we have Act'= y(act-3031) Here change in position in Bill's frame of reference is 0x=0 :.. Act' = Pact → At' = Ø 4t => st ' = 44'/7-Y?

where 8 = Lostentz factor and ß = X : change in time 4t• at'/i-v2 V2 2

) Now from Bill's frame of reference Abby travells for at time in a velocity. o the distance travelled by Abby is davat the time taken by the signal to travel this a distance is t = d - Eat] this is the required time. signal travel in speed of light i.ee. :-* - ğ it' side