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

Answer:

v = 0.92 c

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

$L_x' = L_x\sqrt{1 - \frac{v^2}{c^2}}$

so along x direction the length will contract

now the angle observed by the observer is given as

$tan\theta' = \frac{L_y}{L_x'}$

$tan75 = \frac{L_o sin55}{L_ocos55\sqrt{1 - \frac{v^2}{c^2}}}$

$3.73 = \frac{1.43}{\sqrt{1 - \frac{v^2}{c^2}}}$

$\sqrt{1 - \frac{v^2}{c^2}} = 0.38$

$v = 0.92 c$