(Solved): The relative speed of O and O' is 0.8c. At t' = 2 x 10-7s, a super bullet is fired from x' = 100 m ...

The relative speed of O and O' is 0.8c. At t' = 2 x 10-7s, a super bullet is fired from x' = 100 m. Traveling in the negative x'-direction with a constant speed, it strikes a target at the origin of O' at r' = 6 x 10-7 s. As determined by O, what is the speed of the bullet and how far did it travel? Ans. 3 x 10¹ m/s; 6.67 m A ground observer determines that it takes 5 x 10-7s. for a rocket to travel between two markers in the ground that are 90 m apart. What is the speed of the rocket as determined by the ground observer? Ans. 0.6c Refer to Problem 6.34. As determined by an observer in the rocket, what is the distance between the two markers and the time interval between passing the two markers? Ans. 72 m; 4 x 10-¹s A laser beam is rotated at 150 rev/min and throws a beam on a screen 50 000 miles away. What is the sweep speed of the beam across the screen? Ans. 7.85 x 105 mi/s (note: since c = 1.86 x 105 mi/s, the sweep speed is larger than c.) - Show that the expressions x² +²+z² - c²1² and dx² + dy² + dz²c²di² are not invariant under Galilean transformations.