The incident was captured by a body camera Goodman was wearing.
The video, which Goodman posted to his Facebook page, shows Noe biking close to the divider line on the road.
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A beep is heard and then a white pickup truck passes before a black Volvo knocks Noe over and speeds off.
Noe got knocked to the ground but quickly climbed to his feet.
Goodman wrote that his friend was taken to a hospital and was doing well because he's "one tough dude."
According to the National Park Service, 58-year-old Marshall Grant Neely III was arrested in connection with the incident.
Records show Neely is the Dean of Students at University School of Nashville and has been placed on administrative leave, WKRN reports.
Neely was booked into the Williamson County Detention Center on Saturday night, where he is charged with reckless endangerment, leaving the scene of an accident, failure to immediately notify of an accident, and failure to render aid. He could face federal charges, too
Storyful contributed to this post.