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Date May 2018 Marks available 2 Reference code 18M.3.SL.TZ1.5
Level Standard level Paper Paper 3 Time zone Time zone 1
Command term Draw Question number 5 Adapted from N/A

Question

An observer on Earth watches rocket A travel away from Earth at a speed of 0.80c. The spacetime diagram shows the worldline of rocket A in the frame of reference of the Earth observer who is at rest at x = 0.

Another rocket, B, departs from the same location as A but later than A at ct = 1.2 km according to the Earth observer. Rocket B travels at a constant speed of 0.60c in the opposite direction to A according to the Earth observer.

Rocket A and rocket B both emit a flash of light that are received simultaneously by the Earth observer. Rocket A emits the flash of light at a time coordinate ct = 1.8 km according to the Earth observer.

Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.

[2]
a.

Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.

[3]
b.

Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.

[2]
c.

Calculate the velocity of rocket B relative to rocket A.

[2]
d.

Markscheme

straight line with negative gradient with vertical intercept at ct = 1.2 «km»

through (–0.6, 2.2) ie gradient = –1.67

M18/4/PHYSI/SP3/ENG/TZ1/05.a/M

 

Tolerance: Allow gradient from interval –2.0 to –1.4, (at ct = 2.2, x from interval 0.5 to 0.7).

If line has positive gradient from interval 1.4 to 2.0 and intercepts at ct = 1.2 km then allow [1 max].

[2 marks]

a.

line for the flash of light from A correctly drawn

line for the flash of light of B correctly drawn

correct reading taken for time of intersection of flash of light and path of B, ct = 2.4 «km»

M18/4/PHYSI/SP3/ENG/TZ1/05.b/M

 

Accept values in the range: 2.2 to 2.6.

[3 marks]

b.

the two events take place in the same point in space at the same time

so all observers will observe the two events to be simultaneous / so zero difference

 

Award the second MP only if the first MP is awarded.

[2 marks]

c.

\(u' = \frac{{ - 0.6 - 0.8}}{{1 - ( - 0.6) \times 0.8}}\)

«»0.95 «c»

[2 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Option A: Relativity » Option A: Relativity (Core topics) » A.3 – Spacetime diagrams
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