Plot, on the axes, the point corresponding to event 2.

Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.

Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly².

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.

Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.

Determine, using the diagram, the speed of the spacecraft relative to the galaxy.

point as shown ✔

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 ✔

100² − 20² = 9600 «ly²» ✔

Also accept 98 (the square root of 9600).

Allow negative value.

9600 = 120² − c²t² ✔

ct = «−» 69.3 «ly» / t = «−» 69.3 «y» ✔

Allow approach with Lorentz transformation.

line from event 2 parallel to $x$’ axis intersects ct’ axis at a negative value ✔

event 2 occurred first ✔

use of tan θ = $\frac{v}{c}$ with the angle between the time axes ✔

to get (0.70 ± 0.02)c ✔

Almost all candidates were able to plot the event on the diagram.

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.

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 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 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.

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.