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

4221 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is an ohmic resistor? How to check if a resistor is ohmic?


An object with weight w is suspended from two strings at angles θ1 and θ2 to the vertical and with tensions T1 and T2. How would you resolve the vertical and horizontal forces?


What is the angular velocity of a car wheel which diameter is d = 15 mm if the car velocity is of 120 km/h?


There is a train A. On the roof of A is another frictionless train B of mass Mb. A mass Mc hangs off the front of A and is attached to the front of B by rope and frictionless pulley. How fast should A accelerate so that B wont fall off the roof of A.


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:

© 2026 by IXL Learning