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Date	November 2017	Marks available	2	Reference code	17N.3.SL.TZ0.5
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Determine	Question number	5	Adapted from	N/A

Question

Two rockets, A and B, are moving towards each other on the same path. From the frame of reference of the Earth, an observer measures the speed of A to be 0.6c and the speed of B to be 0.4c. According to the observer on Earth, the distance between A and B is 6.0 x 10⁸ m.

Define frame of reference.

[1]

a.

Calculate, according to the observer on Earth, the time taken for A and B to meet.

[2]

b.

Identify the terms in the formula.

u′ = $\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}$

[1]

c.

Determine, according to an observer in A, the velocity of B.

[2]

d.

Determine, according to an observer in A, the time taken for B to meet A.

[2]

e.i.

Deduce, without further calculation, how the time taken for A to meet B, according to an observer in B, compares with the time taken for the same event according to an observer in A.

[2]

e.ii.

Markscheme

a co-ordinate system in which measurements «of distance and time» can be made

Ignore any mention to inertial reference frame.

a.

closing speed = c

2 «s»

b.

u and v are velocities with respect to the same frame of reference/Earth AND u′ the relative velocity

Accept 0.4c and 0.6c for u and v

c.

$\frac{{ - 0.4 - 0.6}}{{1 + 0.24}}$

«–» 0.81c

d.

$\gamma$ = 1.25

so the time is t = 1.6 «s»

e.i.

gamma is smaller for B

so time is greater than for A

e.ii.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.

[N/A]

e.i.

[N/A]

e.ii.

Syllabus sections

Option A: Relativity » Option A: Relativity (Core topics) » A.2 – Lorentz transformations

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