  The performance of the proposed MATHUSLA detector as an instrument for
studying the physics of cosmic rays by measuring extensive air showers is
presented. The MATHUSLA detector is designed to observe and study the decay of
long-lived particles produced at the pp interaction point of the CMS detector
at CERN during the HL-LHC data-taking period. The proposed MATHUSLA detector
will be composed of many layers of long scintillating bars that cannot measure
more than one hit per bar and correctly report the hit coordinate in case of
multiple hits. This study shows that adding a layer of RPC detectors with both
analogue and digital readout significantly enhances the capabilities of
MATHUSLA to measure the local densities and arrival times of charged particles
at the front of air showers. We discuss open issues in cosmic-ray physics that
the proposed MATHUSLA detector with an additional layer of RPC detectors could
address and conclude by comparing with other air-shower facilities that measure
cosmic rays in the PeV energy range.
