In the two-match series against the Kiwis, Archer took only a couple of wickets at an average of over 100.
Archer's bouncer evaded Kane's helmet by a whisker.
Root is confident that Archer will come back strongly after a lean series in New Zealand.
Archer was racially abused by a member in the crowd during the first Test.
Kane Williamson didn't give any chance to England thereafter and notched up his 21st Test century.
England is currently playing 2nd Test at Seddon Park in Hamilton.
The 116-run stand between Latham and Ross Taylor helped the hosts recover from a jittery start.
Archer was at the receiving end of ‘racial insults’ while batting.
Archer received an apology from New Zealand Cricket chief David White.
The England and New Zealand cricket boards are investigating the incident.