Calculate the length of a 120m (as measured by the astronaut) spaceship travelling at 0.85c as measured by a stationary observer

The length of the spaceship of 120m was measured at rest relative to the spaceship so we will take that as the proper length, dennoted Lproper
We first calculate the Lorentz factor:
Ɣ = 1/sqrt(1-(v/c)2)
Ɣ = 1/sqrt(1-0.852)
Ɣ = 1.8986... (Keep this number in your calculator as rounding now will affect your final answer)
Now, relate this to the formula for length contraction:
L = Lproper / Ɣ
L = 120/1.8986...
L = 63.2m as measured by the stationary observer

KM
Answered by Kerr M. Physics tutor

3884 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Two cars start at point A. Car 1 moves in a direction at 5 m/s. After 10 seconds car 2 accelerates in the same direction as car 1 at 2m/s^2. At what time after car 1 starts moving and distance from A does car 2 pass car 1?


A bullet is fired horizontally from a gun at a height of 1.5m at 280m/s. Calculate the time taken for it to hit the ground. A second bullet is fired from an adjacent gun at 370m/s. Calculate the distance it travel before the first bullet hits the ground.


Assuming the Earth is a perfect sphere of radius R. By how much would your mass (m), as given by a scale, change if you measured it on the north pole and on the equator?


How does a capacitor work and how do I treat it in a circuit?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning