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Date May 2011 Marks available 2 Reference code 11M.3.SL.TZ2.10
Level Standard level Paper Paper 3 Time zone Time zone 2
Command term Calculate Question number 10 Adapted from N/A

Question

This question is about relativity.

Carrie is in a spaceship that is travelling towards a star in a straight-line at constant velocity as observed by Peter. Peter is at rest relative to the star.

Carrie measures her spaceship to have a length of 100m. Peter measures Carrie’s spaceship to have a length of 91m.

(i) Explain why Carrie measures the proper length of the spaceship.

(ii) Show that Carrie travels at a speed of approximately 0.4 c relative to Peter.

[3]
a.

According to Carrie, it takes the star ten years to reach her. Using your answer to (a)(ii), calculate the distance to the star as measured by Peter.

[2]
b.

According to Peter, as Carrie passes the star she sends a radio signal. Determine the time, as measured by Carrie, for the message to reach Peter.

[3]
c.

Markscheme

(i) proper length is measured by observer at rest relative to object / Carrie is at rest relative to spaceship;

(ii) \(\gamma  = \left( {\frac{{100}}{{91}} = } \right)1.1\);
evidence of algebraic manipulation e.g. \(\frac{{{v^2}}}{{{c^2}}} = 1 - \frac{1}{{{{1.1}^2}}}\) to give v=0.42c;
≈0.4c

a.

travel time measured by Peter = (10×γ=)11years;
4.6ly or 4.4ly (if 0.4 c used);

b.

moves away at 0.42 c so is 4.2ly away when signal emitted; (allow ECF from (a)(ii))
signal travel time t where ct=4.2+0.42ct;
7.2y or 7y (if 0.4 c used);

c.

Examiners report

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

Syllabus sections

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