I always thought of a hike as being more of a "mountain-based" activity.
Hence the "Go take a hike, buddy" translates to wishing someone an exhausting uphill walk, which also removes them from your sight once they went over the mountain.
Ok, now I'm curious, gonna look this shit up. 

 Well the mountain part is somewhat correct but when I tried to look up the expression which it doesn't seem to specifically mention mountains. Must be a gap in the records.