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Solutions e3

# Solutions e3 - TOP NEWS STORIES Late Working NASA...

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Exam #3 practice problems solutions Physics 204 summer 2008 1. NASA makes an announcement that the Hubble Space Telescope has detected a signal from an alien probe. When the probe sent the signal it was (light years 0.20 ly 1 ) away and headed towards Earth at . 0.75 c a. By the time the signal reaches Earth how far away is the probe? How much time will pass on earth between the signal being received and the probe arriving? b. At the moment the probe sends the signal, how far away does the probe detect the earth to be? c. From the moment the probe sends the signal, how long will the probe take to reach the earth according to its own clock? Since the speed of light is finite, the light that was emitted by the probe when it was away took 0.20 ly 0.20 yr to arrive. During that time the probe traveled ( )( ) 0.75 0.20 0.15 d vt c yr ly = = = 0.05 ly . By the time the light reaches Earth the probe will be only away. This means the probe will arrive at Earth in ( ) ( ) 0.05 0.75 0.067 t d v ly c yr = = = Because of length contraction, from the probe’s point of view the earth is only ( ) ( ) ( ) 0.132 2 2 1 1 0.75 0.20 p x v c x Δ = Δ = 0.75 c ly ly = away. ( ) ( ) 0.132 0.75 0.176 v ly c yr = = = t d to reach Earth. At it will take the probe 2. In order to investigate the alien probe featured in the previous problem NASA launches a probe of its own. It speeds away from Earth at . 0.60 c a. How fast is the alien probe moving relative to NASA’s probe? b. Unfortunately the alien probe is highly maneuverable and slips past NASA’s probe. NASA’s probe turns around and pursues the alien probe but can’t keep up due to its slower speed. How fast is the alien probe moving relative to NASA’s probe now? 0.60 NE v c = 0.75 AE v c = − ( ) ( ) ( )( ) 2 2 2 0.75 0.60 0.93 0.75 0.60 1 1 1 AE EN AE NE AN AE EN AE NE c c v v v v v c v v v v c c c c c + = = = = − + The result was negative because of the coordinate system I used. The alien probe is moving to the left from the point of view of NASA’s probe. Once the alien probe slips past NASA’s probe… 1 A light year is the distance that light travels in 1 year. Earth x NASA's probe Alien probe 0.60 NE v c = − 0.75 AE v c = − Earth x NASA's probe Alien probe

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