25. A K meson at rest decays into andn particles each having a speed of 0.85...

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25. A K° meson at rest decays into andn particles each having a speed of 0.85 c. If a K° meson travelling at a speed of 0.9 c decays, what is the maximum speed one of the pions can have? What is the least speed? (Ans. 0.9915 c, 0.212 c) 26. An observer in frame S observes a photon travelling in a direction making 60° with the X-axis. A frame S' travels with a speed 0.6 c along the common X - X' axis. What angle does the photon make with the X'-axis as observed by an observer in S'? (Ans. 81.8° above the negative X'-axis) Hint: U, = 0.500c, U, = 0.866c. Find U,U, and tan 0' = U 27. A space traveller on a rocket notes that he is travelling towards a star 1 light year away from the earth with a speed v. An observer on earth finds that the rocket is travelling with a speed v but says the star is 10 light years away. (a) How long does the trip last according to the space traveller? (b) How long does the trip last according to the observer on the earth? Who is correct? (Ans. (a) 1.0005 y (b) 10.05 y. Both are correct) 25. A K° meson at rest decays into andn particles each having a speed of 0.85 c. If a K° meson travelling at a speed of 0.9 c decays, what is the maximum speed one of the pions can have? What is the least speed? (Ans. 0.9915 c, 0.212 c) 26. An observer in frame S observes a photon travelling in a direction making 60° with the X-axis. A frame S' travels with a speed 0.6 c along the common X - X' axis. What angle does the photon make with the X'-axis as observed by an observer in S'? (Ans. 81.8° above the negative X'-axis) Hint: U, = 0.500c, U, = 0.866c. Find U,U, and tan 0' = U 27. A space traveller on a rocket notes that he is travelling towards a star 1 light year away from the earth with a speed v. An observer on earth finds that the rocket is travelling with a speed v but says the star is 10 light years away. (a) How long does the trip last according to the space traveller? (b) How long does the trip last according to the observer on the earth? Who is correct? (Ans. (a) 1.0005 y (b) 10.05 y. Both are correct)

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