A rod of length Lo moves iwth a speed v along the horizontal direction. The rod makes an angle of (θ)0 with respect to the x' axis. Required:
a. Show that the length of the rod as measured by a stationary observer is L=L0[1-v^2/c^2 cos^2(θ)0].
b. Show that the angle the rod makes iwth the x-axis is given by the expression tan(theta)=tan(θ)0/(1-v^2/c^2)^.5

From the question we are told that

  The length of the rod is  

    The  speed is  v  

     The angle made by the rod is  

Generally the x-component of the rod's length is  

Generally the length of the rod along the x-axis  as seen by the observer, is mathematically defined by the theory of  relativity as

=>    

Generally the y-component of the rods length  is mathematically represented as

Generally the length of the rod along the y-axis  as seen by the observer, is   also equivalent to the actual  length of the rod along the y-axis i.e

    Generally the resultant length of the rod as seen by the observer is mathematically represented as

=>  

=>  

=>  

=>

=>

=>

Hence the length of the rod as measured by a stationary observer is

   Generally the angle made is mathematically represented

=>  

=>

Explanation: