Question

if you shoot a cannonball due north from a latitude of -45o where will it fall 100km from the cannon

Answer 1

At a more northern latitude, but still in the southern hemisphere. Figure out how many degrees of longitude correspond to 100 km and add it to -45. It's roughly one degree.

Is this really what they are considering astronomy these days?

Answer 2

I should have said degrees of latitude, not longitude.

One degree of either is about 111 km.

100 km is therefore 0.901 degrees