Question 19M.3.SL.TZ1.5
| Date | May 2019 | Marks available | [Maximum mark: 10] | Reference code | 19M.3.SL.TZ1.5 |
| Level | SL | Paper | 3 | Time zone | TZ1 |
| Command term | Determine, Plot, Show that, Suggest | Question number | 5 | Adapted from | N/A |
The diagram shows space and time axes and ct for an observer at rest with respect to a galaxy. A spacecraft moving through the galaxy has space and time axes ′ and ct′.
A rocket is launched towards the right from the spacecraft when it is at the origin of the axes. This is labelled event 1 on the spacetime diagram. Event 2 is an asteroid exploding at = 100 ly and ct = 20 ly.
Plot, on the axes, the point corresponding to event 2.
[1]
point as shown ✔
Almost all candidates were able to plot the event on the diagram.
Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.
[2]
ALTERNATIVE 1
the rocket would have to travel faster than the speed of light ✔
so impossible ✔
ALTERNATIVE 2
drawing of future lightcone at origin ✔
and seeing that the asteroid explodes outside the lightcone so impossible ✔
ALTERNATIVE 3
the event was observed at +20 years, but its distance (stationary) is 100 ly ✔
so the asteroid event happened 80 years before t = 0 for the galactic observer ✔
Most of the candidates identified, that the spacecraft was launched after the asteroid explosion and better candidates were also able to explain their reasoning with a drawing of light cones on the spacetime graph being the most popular response type.
Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly2.
[1]
1002 − 202 = 9600 «ly2» ✔
Also accept 98 (the square root of 9600).
Allow negative value.
Most of the candidates well used the formula for invariant spacetime from the data booklet, but only a few strong candidates were able to determine the time between the events according to the spacecraft observer. This implies a lack of understanding of the concept of invariance for different frames of reference.
An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart. Determine, according to the spacecraft observer, the time between events 1 and 2.
[2]
9600 = 1202 − c2t2 ✔
ct = «−» 69.3 «ly» / t = «−» 69.3 «y» ✔
Allow approach with Lorentz transformation.
Most of the candidates well used the formula for invariant spacetime from the data booklet, but only a few strong candidates were able to determine the time between the events according to the spacecraft observer. This implies a lack of understanding of the concept of invariance for different frames of reference.
Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.
[2]
line from event 2 parallel to ’ axis intersects ct’ axis at a negative value ✔
event 2 occurred first ✔
Most of the candidates well used the formula for invariant spacetime from the data booklet, but only a few strong candidates were able to determine the time between the events according to the spacecraft observer. This implies a lack of understanding of the concept of invariance for different frames of reference. Most candidates well determined that event 2 occurred first in d ii), with a lesser number showing this correctly via the spacetime diagram.
Determine, using the diagram, the speed of the spacecraft relative to the galaxy.
[2]
use of tan θ = with the angle between the time axes ✔
to get (0.70 ± 0.02)c ✔
Many candidates determined the speed using the spacetime diagram. However, some experienced difficulties reading accurately from the graph, and though their approach was correct, they failed to gain a result within the accepted range of values.