Physics - Special Relativity

Question

Fred travels past Alice at a constant speed of 0.886c in the positive x direction. Fred is holding a meter stick at an angle of 38.8° with respect to the +x axis. What is the length (in m) and orientation (in degrees) of the meter stick according to Alice?

Answer 1

Length contractions affect only the meter stick component that is parallel to the motion.  The meter stick component which is perpendicular to the motion is unchanged.

 

Meter stick vector components in Fred's reference frame

x-direction: cos(38.8º)

y-direction: sin(38.8º)

 

Meter stick vector components in Alice's reference frame
x-direction: cos(38.8º)⋅SQRT[1-(0.866)²] = 0.195 m
y-direction: sin(38.8º)=0.626 m

 

The length of the meter stick according to Alice is

l = SQRT[(0.195)2  + (0.626)²]= 0.656 m

and the angle of the meter stick with respect to the x-axis according to Alice is

θ = tan^-1(0.626/0.195) = 72.7º