Maybe you meant Chinese, then Vikings, then Spanish....?
With “bow and arrow”, do you mean the crossbow...or longbow? 9thC is a little early for longbow, I believe
The Spanish hired the most advanced surveyors on the planet to do a grand basic survey of North America ~ besides, they knew it got cold out there ~ so they hired people who could survive it.
All the various markers in the midwest that have runic writing are where they ought to be for survey benchmarks, and the one at Heavener OK, in fact, says it's a benchmark or boundary stone. The one at Kensington refers to the then King of Spain to give us a date when it was set.
From about 1555 through 1609 North America East of the MIssissippi was in the grip of a 70 year period of substantially reduced rainfall, and Virginia actually suffered 17 full years of ZERO rainfall within that period.
It was pretty obvious to the Spanish that the Mid Atlantic was a horrid wasteland so they didn't do much around here.
However they moved up the Mississippi and began mining operations ~ we all know about those ~ but they also laid out towns/villages ~ and brought cattle, horses, chickens, ducks, and a number of pig varieties that can be typed to various regional domestications that took place in Europe and the Middle East over the last 15000 years.
They even created a map (which I haven't found yet) that shows the location of every single bench mark they put in place. They identified the benchmarks with a special name. All the gazeteers show where those marks are.
The Spanish, like the Chinese before them, readily found the main course of the MIssissippi through the delta country ~ so anything you hear about the French discovering that route is a misconstruction of what was actually said. The Spanish knew where it was but wouldn't tell the French, so the French found it on their own opening up the secret to others.
The Shawnee indians owned the falls on the OHio (Where lOuisville is) This forced the Spanish to cut up the Wabsh to the White rivers to detour around the falls. There's a 2 mile portage that takes you to the Miami river, and that gets you back into the ohio about Cincy. From there up to Columbus OHio there was a navigable stream that ends just West of the the OLd Stone Fort ~ which looks pretty Spanish to my untrained eye (but, of course, I found duplicates by looking for Spanish structures from the 1500-1700 period).
Just darn, those guys were here first ~ and they hired Viking descendants ~ none of which is a surprise.
The Vikings didn't have their design for their north atlantic capable boats until after they'd made permanent contact with the Sa'ami ~ who came up with a working design.
So, who brought the bow and arrow at 800 AD, and who sailed here in a boat that wasn't invented for another 150 years?
Oh! Oh! Oh! I can answer this, since I just read "Longbow: A Social and Military History" by Robert Hardy! Your definition of a "longbow" may be too narrow if you restrict it to bows that are about 6' long, made of yew (both heart and sap wood) and have a D-shaped cross-section.
They have the remains of bows, that would have been approximately 6 ft. in length, that they dug up in Somerset, England. These two bows date to around 2,400 B.C. He also cited examples of longbows from Egypt, other parts of Africa, Asia and, most relevantly to this thread, the cold Nordic regions.
These longbows differed, in many respects (length, wood used and cross-section, for example), to the longbows used by Henry V to obliterate the French at Agincourt, but that weapon itself had evolved from the time Edward I faced the Welsh longbow, a century earlier and those bows were probably different, in some ways, to the examples pulled from the wreck of the "Mary Rose" of 1545.
Interestingly, there was speculation that the Vikings may have re-introduced the longbow to Britain during their occupation of parts of that island.