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Date	November 2018	Marks available	3	Reference code	18N.3.SL.TZ0.4
Level	Standard level	Paper	Paper 3	Time zone	0 - no time zone
Command term	Determine	Question number	4	Adapted from	N/A

Question

A rocket of proper length 120 m moves to the right with speed 0.82c relative to the ground.

A probe is released from the back of the rocket at speed 0.40c relative to the rocket.

Calculate the speed of the probe relative to the ground.

[2]

a.

Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.

[2]

b.i.

Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.

[3]

b.ii.

Markscheme

$\frac{0.82 c + 0.40 c}{1 + \frac{0.82 c \times 0.40 c}{c^{2}}}$ $\frac{{0.82c + 0.40c}}{{1 + \frac{{0.82c \times 0.40c}}{{{c^2}}}}}$ ✔

0.92c ✔

a.

$\Delta t' = \frac{{120}}{{0.40c}}$ ✔

$\Delta t' = 1.0 \times {10^{ - 6}}$ «s» ✔

b.i.

$\gamma =$ « $\frac{1}{{\sqrt {1 - {{0.82}^2}} }} =$ » 1.747 ✔

Δt = « $\gamma \left( {\Delta t' + \frac{{v\Delta x'}}{{{c^2}}}} \right)$ » = $1.747 \times \left( {1.0 \times {{10}^{ - 6}} + \frac{{0.82c \times 120}}{{{c^2}}}} \right)$

OR

Δt = $\frac{{120}}{{1.747 \times \left( {0.92 - 0.82} \right)c}}$ ✔

2.3 × 10⁻⁶ «s» ✔

b.ii.

Examiners report

[N/A]

a.

[N/A]

b.i.

[N/A]

b.ii.

Syllabus sections

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

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