Will a fired bullet hit the ground at the same time as a dropped bullet?

[Sentryduty]

Q1, How far will a .45 ACP travel before striking the ground if fired level from hip height?

Plugging some numbers, hip height? 1 meter perhaps, velocity of a .45 ACP, 230gr ball 270 m/s @ muzzle 5" test barrel.

Rate of fall for a .45 ACP round dropped at 1m:

Speed at impact:4.43 m/s
or 15.94 km/h
Time until impact: 0.45 s
Energy at impact: 0.15 joules

270*0.45s = 121.5m (not accounting for horizontal deceleration of the projectile, and subsequent reduction in travel range)

Due to the earth being spherical, the dropped round will travel a shorter vertical distance than the fired round, as optically level does not account for the geoid model. Even built level ground in not truly level, it is slightly curved. Rough math suggests the fired projectile will have to travel an additional 12 millimetres vertically to reach the ground.

Re-running the calculations shows this does not change the travel time to the nearest hundredth of a second.

Q2, Do they fall at the same rate?
This is a tricky bit to remember, however, I will say they should fall at the same rate, negating wind resistance on the projectile shape, both should accelerate vertically at -9.8 m/s2 at 1 m height terminal velocity will not yet be reached.

There is my mental exercise for the day, I am curious to see the answers, and gather what I've missed.

As we used to joke in the survey world, "F**k it, close enough".