| Date | May 2013 | Marks available | 4 | Reference code | 13M.3.HL.TZ1.14 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 1 |
| Command term | Calculate and Deduce | Question number | 14 | Adapted from | N/A |
Question
This question is about relativistic kinematics.
Speedy is in a spacecraft being chased by Police Officer Sylvester. In Officer Sylvester’s frame of reference, Speedy is moving directly towards Officer Sylvester at 0.25c.
Officer Sylvester switches on the blue flashing lamps on his police spacecraft.
(i) Calculate, assuming that a Galilean transformation applies to this situation, the value of the speed of the light that Speedy would measure using the flashing lamps.
(ii) Speedy measures the speed of the light emitted by the flashing lamps. Deduce, using the relativistic addition of velocities, that Speedy will obtain a value for the speed of light equal to c.
Markscheme
(i) 1.25c
(ii) \(v' = \frac{{c - v}}{{1 - \frac{{cv}}{{{c^2}}}}}\);
\( = \frac{{0.75c}}{{1 - 0.25}}\);
shows that fraction = c;
Award [2 max] if signs incorrect.
Examiners report
Most candidates answered (b)(i) correctly. Many candidates refused to put an answer greater than c because that is impossible, missing the point of the question (that the Galilean transformation gives a wrong answer so the relativistic transformation is required).
In (b)(ii) most candidates got the signs wrong and so scored two marks out of three.
