Question

A stick with a proper length l₀ is moving past a stationary frame S with V = c/2. In the frame S′ of the stick, the angle between the stick and its direction of motion is φ₀ = 45^◦ . Find the length of the stick and the angle it makes to its velocity, as measured in the frame S. (relativity)

Answer 1

The x component of the length in the S' frame is given by
   
And y component of the length in the S' frame is given by
  
And in the S frame, the rod is moving with velocity, v = c/2. So, the length in the S frame is
  
And the y component does not transform, so,
  
Given the values, we have


And

So, the length of the stick in the frame S is
  

And the angle it makes with velocity is