1. A police radar gun operates at a frequency of 10.5 GHz. The of?cer, sitting in a patrol car at rest by the highway, directs the radar beam toward a speeding car traveling 80 mph directly away from the patrol car. What is the frequency shift of the re?ected beam, relative to the original radar beam?
2. A spaceship moving 0.80c direction away from Earth ?res a missile that the spaceship measures to be moving at 0.80c perpendicular to the ship's direction of the greatest and least speeds that the mesons may have?
3. Frank and Mary are twins, and Mary wants to travel to our nearest star system, Alpha Centauri (4.30 lightyears away). Mary leaves on her 30th birthday and intends to return to Earth on her 52nd birthday.
(a) Assuming her spaceship returns from Alpha Centauri without stopping, how fast must her spaceship travel?
(b) How old will Frank be when she returns?