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

[WarPig1976]

A little fun for the crew to consider. A popular T.V program ran an episode a number of years back that answers these questions. I'll post their results after a day or so to give those who wish to play along time to guess.

Two questions, How far do you think a .45 ACP bullet will travel if the muzzle is perfectly level at firing at about waist level?
Will a perfectly level fired bullet and a dropped bullet hit the ground at the same time if they're fired/dropped from the exact same height and instant?

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[Peter Laidler]

Can't answer the first bit, but the second Q. is NO. If I am reading the Q correctly, can I assume that you are in a balloon high above the desert looking down? The reason being that the bullet DROPPED downwards will accelerate to terminal velocity (t/v) and continue at this t/v rate until it hits the ground. However, the bullet FIRED downwards will decelerate, albeit slowly until it reaches t/v. Then it'll simply continue at this speed until it hits the ground. Clearly, the fired bullet has had an initial advantage that gravity couldn't prevent. But in either case, at 230g, I wouldn't try catching them!

Just me with my ex part-time Physics teachers hat on

[browningautorifle]

But Peter, according to the theories...the bullets should be falling at the same speed...and we're only dealing with say, a meter. The forward movement shouldn't matter and the downward movement should be the same because of gravity. If you deal with a perfect vacuum and a perfect plain then in theory they should strike at the same time...? I too used to teach these things and the troops informed me I was teaching physics... Neat...

The first question depends on muzzle height when the bullet is fired. At 48" height, which should be the height of an M1 Thompson when you fir from the shoulder, the tables are available for bullet drop and trajectory...without getting a pencil sharpener out...

[WarPig1976]

bullet FIRED downwards

The bullet is fired perfectly level not downward.

[browningautorifle]

Level...RTFQ... Get your pencil out Peter...

[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".

[browningautorifle]

How far do you think a .45 ACP bullet will travel if the muzzle is perfectly level at firing at about waist level?

He meant distance from the firer...like 100m, 200m?

negating wind resistance on the projectile shape,

The perfect plane, in a vacuum...things that can't physically be done. All theory...

[Sentryduty]

The perfect plane, in a vacuum...things that can't physically be done. All theory...

Indeed, it's a blackboard physics game, "if two identical snowflakes..."

To break the basic questions back down, I see: how far would a bullet travel on the level before plowing into the dirt? and does the action of firing a bullet perpendicular to the earth defy gravity?

Based on that breakdown, I say not more than 121.5 metres (based on my assumptions of mass etc) and NO shooting a bullet doesn't defy gravity. Shooting upwards only overcomes gravity.

Now I am reminded of the charts of sight adjustments based on shooting uphill vs downhill spring to mind and other tidbits of info, stuff I may never use again actually.

[Peter Laidler]

But I did quantrify my answer with an assuming question first. By LEVEL did he mean lever vertically or level horizontally? And he did ask if A bullet would.... When if he was meaning in relation to the first part of the Q, he should have said THE bullet. And I did explain the reason for answering the Q in the way it appeared to be asked.

Remember the old teaching basics. If a question can elicit a wrong answer, then the teacher is at fault.

Like 'Q...... what do tanks run on' A.Tracks. Or is it Roads or is it Petrol?

[Gil Boyd]

WTF is this debate about its self explanatory or am I being thick? I'm probably on my own as always!