The limitations of common sense

Common sense tells me that the firing of the projectile is like throwing a ball in a car.The projectile starts out with the initial velocity of the earth as well as the velocity imparted by firing it so it'll land in roughly the same spot as where it is fired from if fired directly up.Now on the other hand if you fired the projectile directly up (from the equator) and managed to stop the earth down to zero at the second it was fired you'd see that projectile fly very far away from where you were initially started. (on top of that you'd probably destroy earth to but who really wants to get into the physics of stopping the earth.)

Oh yeah how do justifiy aproximatly 1000 mph on the equator anyways? (for completeness so people don't think you pulled it out of thin air).

i.e. your taking the circumfrence of the earth and dividing by the time span it takes to go through one complete rotation to arrive at the aproximate linear velocity. (just for clarification sakes and for being specific)