Question

A measuring stick makes an angle of 55° with respect to the x-axis. An observer moving along the x direction measures the angle as 75°. What is the velocity of the observer in units of c?

Answer 1

v = 0.92 c

Step-by-step explanation:

Let the actual length of the rod is L

now its two components along X and Y direction is given as

`L_x = Lcos55`

`L_y = Lsin55`

now by the concept of relativity we know that

`L_x' = L_x\sqrt{1 - (v^2)/(c^2)}`

so along x direction the length will contract

now the angle observed by the observer is given as

`tan\theta' = (L_y)/(L_x')`

`tan75 = \frac{L_o sin55}{L_ocos55\sqrt{1 - (v^2)/(c^2)}}`

`3.73 = \frac{1.43}{\sqrt{1 - (v^2)/(c^2)}}`

`\sqrt{1 - (v^2)/(c^2)} = 0.38`

`v = 0.92 c`