| Date | May 2016 | Marks available | 2 | Reference code | 16M.3.HL.TZ0.6 |
| Level | Higher level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Calculate | Question number | 6 | Adapted from | N/A |
Question
An observer on Earth watches two rockets, A and B. The spacetime diagram shows part of the motion of A and B in the reference frame of the Earth observer. A and B are travelling in the same direction.
For the reference frame of the Earth observer, calculate the speed of rocket A in terms of the speed of light c.
One rocket passes the other at event E. For the reference frame of the Earth observer, estimate
(i) the space coordinate of E, in kilometres.
(ii) the time coordinate of E, in seconds.
Three flashing light beacons, X, Y and Z, are used to guide another rocket C. The flash events are shown on the spacetime diagram. The diagram shows the axes for the reference frames of Earth and of rocket C. The Earth observer is at the origin.
Using the graph opposite, deduce the order in which
(i) the beacons flash in the reference frame of rocket C.
(ii) the Earth observer sees the beacons flash.
Markscheme
Δct=2.0km AND Δx=1.2km
\(v = \ll \frac{{\Delta x}}{{\Delta ct}} = \frac{{1.2}}{{2.0}} \gg = 0.60{\rm{c}}\)
Allow any correct read-off from graph.
Accept answers from 0.57c to 0.63c.
(i) 1.6km
Allow ±0.1km.
(ii) 8.8 μs
Allow ±0.5 μs.
Allow ECF, the answer can be calculated from answers to (a) and (b)(i).
(i) events at same perpendicular distance from x′ axis of rocket are simultaneous OR line joining X to Y is parallel to x′ axis
X and Y simultaneously then Z
MP1 may be present on spacetime diagram.
(ii) constructs light cones to intersect worldline of observer
X first followed by Y and Z simultaneously
Only Y and Z light cones need to be seen.
