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HW_rel - :1 H A friend of yours who is the same age as you...

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Unformatted text preview: (:1) H A friend of yours who is the same age as you trav- e s to the star Alpha Centauri, which is 4 lightryears away and returns inunediateljv. He claims that the entire trip took just 6 3*. How fast did he travel? I I A beam of unstable particles emerges from the exit slit of an accelerator with a speed of 0.89c. Particle detectors 3.0 and 6.0 m from the exit slit measure beam intensities of 2 X 105 particles/cmf-s and 5 X It]? particlesfcmE-s, respec~ lively. (:1) Find the proper half~life of the particles. (it) Deter- mine the beam intensitv at the exit slit of the accelerator. {c} The accelerator is adjusted so that the particles emerge from the exit slit with a speed of 8.96; The beam intensity at the farther detector is again 5 3-: 1t]? particlesfcmE-s. Find the beam mtensity at the exit slit of the accelerator. 32 s I How fast must you be moving toward a red light (a = 650 nm) for it to appear green (it = 525 nm)? '43 u A particle moves with speed 0.8:: along the x” axis o frame 5",. which moves with speed 0.8:“: along the x' axis relative to frame 8’. Frame 5’ moves with speed 0.3c along the x axis relative to frame 5. (c) Find the speed of the particle relative to frame 3’. {ti} Find the speed of the particle relative to frame 5. u A rocket with a proper length of 1000 or moves in .- - + x direction at 0.6c with respect to an observer on the ground. An astronaut stands at the rear of the rocket and fires a bullet toward the front of the rocket at {LSc relative to the rocket. How long does it take the bullet to reach the front of the rocket {a} as measured in the frame of the rocket, (b) as measured in the frame of the ground, and (c) as measured in the frame of the bullet? ...
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