homework and exercises - A big cannon to match a ballistic missile?

During the last years of WW2 the Germans used ballistic missiles V-2 (with payload mass ~1,000 kg) to bombard London, from a distance about 300 km away. Suppose the British could respond by building a cannon of a very large size, to shoot back conventional projectiles. Would this be realistic? Neglecting the air, the maximum projectile range (shot at 45 degrees to the horizon) is $R=V^2/g$, where $V$ is the projectile muzzle velocity. For $R$=300,000 m and $g$=10 m$^2$/s one needs $V$=1,700 m/s. This is on the high side but within the reach for conventional rifles and cannons. Does the presence of the Earth atmosphere make it practically impossible to shoot projectiles at such large distances? Since the air resistance should scale with the projectile cross-section, $F \sim \rho V^2 A$, can a very long and thin hypersonic projectile travel easily through the atmosphere?