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Date May 2011 Marks available 2 Reference code 11M.3.HL.TZ1.17
Level Higher level Paper Paper 3 Time zone Time zone 1
Command term Determine Question number 17 Adapted from N/A

Question

This question is about relative velocities and energy at relativistic speeds.

Two identical rockets are moving along the same straight line as viewed from Earth. Rocket 1 is moving away from the Earth at speed 0.80 c relative to the Earth and rocket 2 is moving away from rocket 1 at speed 0.60 c relative to rocket 1.

Calculate the velocity of rocket 2 relative to the Earth, using the

(i) Galilean transformation equation.

(ii) relativistic transformation equation.

[3]
a.

Comment on your answers in (a).

[2]
b.

The rest mass of rocket 1 is 1.0×103kg. Determine the relativistic kinetic energy of rocket 1, as measured by an observer on Earth.

[2]
c.

Markscheme

(i) u'x= ux + v = 0.60c + 0.80c = 1.40c;

(ii) ux(=ux+v1+uxvc2)=0.60c+0.80c1+0.60c×0.80cc2;
(=1.40c1.48)=0.95c;
Award [1] for answers that use v = –0.80 c to get an answer of –0.38 c.

a.

the answer to (a)(i) exceeds c / the answer to (a)(ii) does not exceed c;
hence the Galilean transformation is not valid / the relativistic transformation must be used / OWTTE;

b.

γ=11v2c2=11=0.802c2c2=1.7;
EK=[γ1]m0c2=[1.6671]×1.0×103×[3.0×108]2;
=6.0×1019J
Award [0] for answers that use Ek = ½ mv2 to get an answer of 2.9×1019 J.

 

c.

Examiners report

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

Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.4 – Relativistic mechanics (HL only)
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