Question 18M.3.SL.TZ1.5
| Date | May 2018 | Marks available | [Maximum mark: 9] | Reference code | 18M.3.SL.TZ1.5 |
| Level | SL | Paper | 3 | Time zone | TZ1 |
| Command term | Calculate, Deduce, Draw, Explain | Question number | 5 | Adapted from | N/A |
An observer on Earth watches rocket A travel away from Earth at a speed of 0.80c. The spacetime diagram shows the worldline of rocket A in the frame of reference of the Earth observer who is at rest at x = 0.
Another rocket, B, departs from the same location as A but later than A at ct = 1.2 km according to the Earth observer. Rocket B travels at a constant speed of 0.60c in the opposite direction to A according to the Earth observer.
Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.
[2]
straight line with negative gradient with vertical intercept at ct = 1.2 «km»
through (–0.6, 2.2) ie gradient = –1.67
Tolerance: Allow gradient from interval –2.0 to –1.4, (at ct = 2.2, x from interval 0.5 to 0.7).
If line has positive gradient from interval 1.4 to 2.0 and intercepts at ct = 1.2 km then allow [1 max].
[2 marks]
Rocket A and rocket B both emit a flash of light that are received simultaneously by the Earth observer. Rocket A emits the flash of light at a time coordinate ct = 1.8 km according to the Earth observer.
Deduce, showing your working on the spacetime diagram, the value of ct according to the Earth observer at which the rocket B emitted its flash of light.
[3]
line for the flash of light from A correctly drawn
line for the flash of light of B correctly drawn
correct reading taken for time of intersection of flash of light and path of B, ct = 2.4 «km»
Accept values in the range: 2.2 to 2.6.
[3 marks]
Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.
[2]
the two events take place in the same point in space at the same time
so all observers will observe the two events to be simultaneous / so zero difference
Award the second MP only if the first MP is awarded.
[2 marks]
Calculate the velocity of rocket B relative to rocket A.
[2]
= «–»0.95 «c»
[2 marks]