104 years ago the https://en.wikipedia.org/wiki/Paris_Gun could shoot 120 km (75 "miles", in medieval units), but it definitely couldn't hit a 200-mm target. Not even in 69 tries. (Yes, it was rifled.)
To me it seems like a more sensible way to hit a target from 7 km away would be to guide the projectile with movable canards, like the VAPP (or, as mentioned elsethread, the M982 Excalibur or XM1156 PGK). You could even do this with a bow and "arrow": once the "arrow" has gained 300 meters of altitude, it has a range of 7 km if its glide ratio is 24, quite achievable (though a regular arrow has a glide ratio of about 0). And you don't have to shoot it straight up, so you can get by with an even lower glide ratio than that.
To me it seems like a more sensible way to hit a target from 7 km away would be to guide the projectile with movable canards, like the VAPP (or, as mentioned elsethread, the M982 Excalibur or XM1156 PGK). You could even do this with a bow and "arrow": once the "arrow" has gained 300 meters of altitude, it has a range of 7 km if its glide ratio is 24, quite achievable (though a regular arrow has a glide ratio of about 0). And you don't have to shoot it straight up, so you can get by with an even lower glide ratio than that.