Q175 · Practice questionComplex familiar6 marks
QUESTION 175 (6 marks)
A spacecraft's crew measures its length as . A laboratory measures its length along its direction of motion as . A clock fixed on the spacecraft records between two ticks.
a)[2 marks]
Identify the proper length and the proper time interval, justifying each choice.
b)[2 marks]
Determine the spacecraft speed as a fraction of .
c)[2 marks]
Determine the laboratory time interval between these ticks.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
(a) and . (b) . (c) .
Worked solution
(a) Proper length is measured in the rest frame of the object, which is the crew's frame. Proper time is measured by a clock present at both events: the two ticks occur at the same position on the spacecraft.
(b) . Therefore .
(c) ; .
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Identify and justify the rest-frame length.
Part a: Identify and justify the proper interval at one spacecraft position.
Part b: Use length contraction with the proper length.
Part b: Calculate the speed fraction.
Part c: Apply time dilation using the same speed.
Part c: Calculate the laboratory interval.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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