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Date	November 2016	Marks available	1	Reference code	16N.3.SL.TZ0.7
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Draw	Question number	7	Adapted from	N/A

Question

Identical twins, A and B, are initially on Earth. Twin A remains on Earth while twin B leaves the Earth at a speed of 0.6c for a return journey to a point three light years from Earth.

Calculate the time taken for the journey in the reference frame of twin A as measured on Earth.

[1]

Determine the time taken for the journey in the reference frame of twin B.

[2]

Draw, for the reference frame of twin A, a spacetime diagram that represents the worldlines for both twins.

[1]

Suggest how the twin paradox arises and how it is resolved.

[2]

Markscheme

«0.6 ct = 6 ly» so t = 10 «years»

Accept: If the 6 ly are considered to be measured from B, then the answer is 12.5 years.

ALTERNATIVE 1

10²− 6²= t²− 0²

so t is 8 «years»
Accept: If the 6 ly are considered to be measured from B, then the answer is 10 years.

ALTERNATIVE 2

gamma is $\frac{5}{4}$

10 × $\frac{4}{5}$ = 8 «years»

Allow ECF from a
Allow ECF for incorrect γ in mp1

three world lines as shown

Award mark only if axes OR world lines are labelled.

according to both twins, it is the other one who is moving fast therefore clock should run slow

Allow explanation in terms of spacetime diagram.

«it is not considered a paradox as» twin B is not always in the same inertial frame of reference

twin B is actually accelerating «and decelerating»

Examiners report

[N/A]

Syllabus sections

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

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19M.3.SL.TZ1.5a: Plot, on the axes, the point corresponding to event 2.
19M.3.SL.TZ2.7b:
Label, with the letter E, the event of the spaceship going past the planet.
18M.3.SL.TZ2.4d.i:
Construct event A and event B on the spacetime diagram.
19M.3.SL.TZ1.5b:
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
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.
16N.3.SL.TZ0.6a:
Calculate the angle between the worldline of S and the worldline of the Earth.
16N.3.SL.TZ0.6c: An event Z is shown on the diagram. Label the co-ordinates of this event in the reference...
18N.3.SL.TZ0.5b.i: Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with...
16N.3.SL.TZ0.6b: Draw, on the diagram, the x′-axis for the reference frame of S.
16N.3.SL.TZ0.7d: Suggest how the twin paradox arises and how it is resolved.
17M.3.SL.TZ1.4d.ii:
Deduce, using the spacetime diagram, which light was turned on first according to observer P.
16N.3.SL.TZ0.7a: Calculate the time taken for the journey in the reference frame of twin A as measured on Earth.
17N.3.SL.TZ0.6d:
For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).
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19N.3.SL.TZ0.4c(ii): Demonstrate using the diagram which lamp, according to observer A, was turned on first.
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.
20N.3.SL.TZ0.5b(ii):
Determine the time, according to spaceship A, when light from event E was observed on spaceship A.
19M.3.SL.TZ1.5e:
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
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Calculate in terms of $c$ the velocity of spaceship A relative to observer O.
20N.3.SL.TZ0.5b(i):
Plot the event E on the spacetime diagram and label it E.
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Draw the time $c t^{'}$ and space $x^{'}$ axes for observer P’s reference frame on the spacetime diagram.
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19M.3.SL.TZ2.7a:
Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80c.

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Option A: Relativity » Option A: Relativity (Core topics)

Option A: Relativity

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