Question

In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 104 km above sea level, a pion is created.The pion has a total energy E of 1.92 × 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

Total energy is given by

where

In its rest frame, pion decays in time . In Earth's frame, pion is moving. Due to relativistic time dilation, the pion decay in time t given by

We will determine the distance covered by the pion before decaying in Earth's frame.

Squaring both sides

The velocity is constant, the distance covered by the pion in time t is

Using 10³m=1km

Initially pion was formed at 104km above the sea level. After traveling 14.4km it decays. The height of the pion when it decay is