Question

This is modern physics question

3. A stick of length L is at rest in a systern O and is oriented at an angle θ with respect to the x axis. An observer in system O' travels at velocity v with respect to the system O along the x axis. What is the apparent angle θ, that the stick makes with the x' axis according to the observer in (? The xxes ae rl

Answer 1

L_x = L cos theta L_y = L sin theta L_y = L_y {perpendicular to velocity so L�_x = L_x squareroot 1 - v^2/c^2 L�_x = L_x squareroot c^2 - v^2/c^2 New lengths are tan alpha = L�_y/L�_x tan alpha = L sin theta/L cos theta c^2 - v^2/c^2 tan alpha = tan theta (c/squareroot c^2 - v^2) alpha = tan^- 1 (tan theta (c/squareroot c^2 - v^2))