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Date	November 2020	Marks available	2	Reference code	20N.3.SL.TZ0.5
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Plot	Question number	5	Adapted from	N/A

Question

The spacetime diagram is in the reference frame of an observer O on Earth. Observer O and spaceship A are at the origin of the spacetime diagram when time $t = t' = 0$ . The worldline for spaceship A is shown.

Event E is the emission of a flash of light. Observer O sees light from the flash when $t = 9$ years and calculates that event E is $4 ly$ away, in the positive $x$ direction.

Calculate in terms of $c$ the velocity of spaceship A relative to observer O.

[1]

a(i).

Draw the $x'$ axis for the reference frame of spaceship A.

[1]

a(ii).

Plot the event E on the spacetime diagram and label it E.

[2]

b(i).

Determine the time, according to spaceship A, when light from event E was observed on spaceship A.

[3]

b(ii).

Markscheme

$0.6 c$ ✓

Accept $1.8 \times 10^{8} m s^{- 1}$ if unit given.

a(i).

line through origin and through $(5, 3) \pm$ one small square at this coordinate ✓

Answers shown for 5(a)(ii) and (b)(i) and (b)(ii).

a(ii).

X value of E at $4$ « $ly$ » ✓

Y value of E at $5$ « $y$ » ✓

b(i).

light cone from E «crosses $c t$ at $9$ so» intersection on $c t' = 5.6 \pm 0.2$ $y$ «on $c t$ scale» ✓

$γ = 1.25$ ✓

so $t' = « \frac{5.6}{1.25} = » 4.5$ « $y$ after leaving Earth» ✓

MP1 accept use of linear equations to find $t = 5.625$

Allow ECF from (b)(i) and (a)

b(ii).

Examiners report

Very well answered.

a(i).

Most answers successfully drew the correct x' axis.

a(ii).

Event E is the event when the light is emitted (4,5). Some candidates missed that and placed it at (4,9).

To determine these coordinates candidates were expected to construct a light path from (0,9) which intercepts at x=4 and t=5. This is a very common mistake which needs careful explanation by teachers.

b(i).

Those candidates who placed E at the correct position were then able to calculate the time appropriately.

b(ii).

Syllabus sections

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

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17M.3.SL.TZ2.5c.i:
On the diagram label the coordinates x and ct.
19M.3.SL.TZ1.5d.ii:
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
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Calculate the angle between the worldline of S and the worldline of the Earth.
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Deduce, using the spacetime diagram, which light was turned on first according to observer P.
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19N.3.SL.TZ0.4c(i):
Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis $x$ '.
19N.3.SL.TZ0.4c(iii): Demonstrate, using the diagram, which lamp observer A observes to light first.
18N.3.SL.TZ0.5b.ii:
Label, on the diagram, the event that has coordinates x′ = 1.0 m and ct′ = 0. Label this event with the letter Q.
18M.3.SL.TZ2.4d.ii:
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
18M.3.SL.TZ1.5a:
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
18M.3.SL.TZ1.5b:
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.
17M.3.SL.TZ2.5c.ii:
State and explain whether the ct coordinate in (c)(i) is less than, equal to or greater than 1.0 m.
16N.3.SL.TZ0.7b:
Determine the time taken for the journey in the reference frame of twin B.
20N.3.SL.TZ0.5a(ii):
Draw the $x'$ axis for the reference frame of spaceship A.
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Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
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Option A: Relativity » Option A: Relativity (Core topics)

Option A: Relativity

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