Question 18M.3.SL.TZ2.d.ii
| Date | May 2018 | Marks available | [Maximum mark: 2] | Reference code | 18M.3.SL.TZ2.d.ii |
| Level | SL | Paper | 3 | Time zone | TZ2 |
| Command term | Estimate | Question number | d.ii | Adapted from | N/A |
When a spaceship passes the Earth, an observer on the Earth and an observer on the spaceship both start clocks. The initial time on both clocks is 12 midnight. The spaceship is travelling at a constant velocity with γ = 1.25. A space station is stationary relative to the Earth and carries clocks that also read Earth time.
Some of the radio signal is reflected at the surface of the Earth and this reflected signal is later detected at the spaceship. The detection of this signal is event B. The spacetime diagram is shown for the Earth, showing the space station and the spaceship. Both axes are drawn to the same scale.
Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.
[2]
ALTERNATIVE 1
«In spaceship frame»
Finds the ratio (or by similar triangles on x or ct axes), value is approximately 4
hence time elapsed ≈ 4 × 90 mins ≈ 6h «so clock time is ≈ 6:00»
Alternative 1:
Allow similar triangles using x-axis or ct-axis, such as from diagrams below
ALTERNATIVE 2
«In Earth frame»
Finds the ratio
, value is approximately 2.5
hence time elapsed ≈ ≈ 6h
«so clocktime is ≈ 6:00»
ALTERNATIVE 2:
[2 marks]