Question

9.1 Lorentz Contraction Objects traveling at relativistic speeds will appear to a stationary observer as shorter, as- suming that it is parallel to the direction of its motion. Using the equation for Lorentz contraction, find the following, where c is the speed of light: a) A spaceship is traveling with a velocity 0.8c. If it is 200m long in its rest frame (when the object is not moving), how long do you observe it to be? Assume that you can see the entire length of the ship edge-on and that you can measure lengths perfectly with your eyes. b) An observer on the spaceship in part a) sees you as it flies by. If you are 1.8m tall in your rest frame, how tall do you appear to the observer on the spaceship? c) You observe a spaceship, which is 100m long in its rest frame, to be 70m long. How fast is the spaceship traveling? Write the velocity in terms of both m/s and in terms of a fraction in c (in decimals, like 0.8c above).

Answer 1

a) Velocity of Spaceship: 0.80 length in reest freame, do = 200m let observed length be= l. So by length contreaction formula we have Yoox -0. - 2004 - 0.64 = 2004 0.36 = 2008 0.6 = 1200 So obsereved dength will be equal to 120m. b) I will appear 1.8m tall to the observere on the Spaceship . As my length of height and motion of spaceship are perpendicular to each othere, so my height will not change. So, I will oppeare 1.8m tall to the observer on the spaceship. c) Given, lo= 100m 1: 70m let speed be r. So by length Controchin foamalo, we have la do stva > 70 = 100 JT - v?

D A 100 Ą | I À 2 V 5/ V100 - so .51c? > V = 0.71410 2. 1424x108 m/s so velocity = 2.14 24 x 10 9 m/s - 0.71410