Question

16. A rod lies parallel to the x axis of reference frame S, moving along this axis at a speed of 0.567c. Its rest length is 2.39 m. What will be its measured length in frame S?

17. In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 131 km above sea level, a pion is created.The pion has a total energy E of 1.61 × 105 MeV and is traveling vertically downward. In the pion's rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth's reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV.

Answer 1

16 )

V = speed of 0.567c

L_o = length = 2.39 m

using

L = L_o ( 1 - V² / C² )^1/2

L = 2.39 X ( 1 - 0.567²C²/C² )^1/2

L = 2.39 X ( 1 - 0.567² )^1/2

L = 1.9686 m

17 )

E = m_o C²

= E / m_o C²

= 1.61 X 10⁵ / 139.6

= 1153.29

we have = ( 1 - v²/c²)^1/2

v/c = ( 1 - 1/1153.29² )^1/2

v/c = 0.999999

t = 1153.29 X 35 X 10^-9  

t = 0.00004036 s

x = v t

x = 0.999999 X 3 X 10⁸ X 0.00004036

x = 12107.987 m

then h = 131000 - 12107.987

h = 118892.013 m

h = 118.892013 km