Bullets

Consider the following ballistics tests:

you are standing on a raft in the middle of the (perfectly calm) pacific ocean somewhere. you fire bullet A parallel to the water around you from shoulder height while at the same time you drop from your hand an identical bullet B from shoulder height. Which bullet hits the water first?

now suppose you run the same experiment on a flat, expansive parking lot. does the same result hold?

i could forsee several plausible answers based on how picky you are with your assumptions.

speaking of water and puzzles, I have one! If u dropped a penny into a bucket of water with 100C heat and another one into an identical bucket with 0C water, which hits the bottom first?

someone's going to alert the moderator for this being off topic, but I'm too lazy to start a new thread, so....

also, the one u firedfrom shoulder height, it'll blow up quickly and fall to the water much fater

Without thinking about it too much.

Assuming the bullet is just a projectile and travels at constant horizontal velocity, so it's all just a matter about vertical distance (assuming the only thing affecting how long the bullet takes to fall is this distance)

Well shoulder height the same in each case, and I'll assume the raft actually has no height above the water at all.

Differences between the two cases. The ocean, despite being flat, is actually slighty curved, whereas the car park is a flat plane. As the gravity helps to act to pull the bullet around the shape of the earth (I'm a chemist, not a physicist - someone can improve on my language), the ditance to fall fired over the ocean is the same as the one dropped.

On the car par, the fired one will have less efective distance to fall, so will hit the ground prior to the dropped one.

Originally posted by Peakite
Without thinking about it too much.

Assuming the bullet is just a projectile and travels at constant horizontal velocity, so it's all just a matter about vertical distance (assuming the only thing affecting how long the bullet takes to fall is this distance)

Well shoulder height the same in each case, and I'll assume the raft actually has no height a ...[text shortened]... d one will have less efective distance to fall, so will hit the ground prior to the dropped one.

Despite having no physics background(I'm a lowly economist):

Isn't it impossible to fire a projectile exactly parallel to the surface of the earth?
Then, the bullet would always be slightly rising (if assumed that he shot perpendicularly to current vertical position) as long as the horizontal velocity is higher than the vertical one.

I would expect the fired bullet to fall slightly later if this is true.

Originally posted by davegage
Consider the following ballistics tests:

you are standing on a raft in the middle of the (perfectly calm) pacific ocean somewhere. you fire bullet A parallel to the water around you from shoulder height while at the same time you drop from your hand an identical bullet B from shoulder height. Which bullet hits the water first?

now suppose you run th ...[text shortened]... d?

i could forsee several plausible answers based on how picky you are with your assumptions.

OK looking at this problem.

We are asked about or assumptions... OK I'm assuming that in both scenarios we can ignore wind resistance etc, and that all other factors are equal for both scenarios. I'll also assume that the bullet isn't fired quickly enought to reach escape velocity.

Now... I think where the crux of the problem lies is... what do you define as a pefectly flat surface? If it's a TRULY flat surface, then it won't follow the contour of the earth (unlike the ocean). Imagine a huge runway 100 miles long, but COMPLETELY FLAT... if the start of the runway is at sea level, the end of the runway will be well over sea-level (several miles at a guess).

Anyway... given these assumptions, the bullet will strike the hard, flat surface first, rather then the ocean... the ocean follows the curve of the earth, whereas a flat solid plane doesn't. 🙂

Originally posted by PawnCurry
OK looking at this problem.

We are asked about or assumptions... OK I'm assuming that in both scenarios we can ignore wind resistance etc, and that all other factors are equal for both scenarios. I'll also assume that the bullet isn't fired quickly enought to reach escape velocity.

Now... I think where the crux of the problem lies is... what do yo ...[text shortened]... n the ocean... the ocean follows the curve of the earth, whereas a flat solid plane doesn't. 🙂

That type of runway doesn't make any sense in the real world, but I agree with you if it's constructed like that.

How big is the raft?

Originally posted by Palynka
[b]Despite having no physics background(I'm a lowly economist):

Isn't it impossible to fire a projectile exactly parallel to the surface of the earth?

I guess to be more clear, I mean that at the instant the bullet is fired, the vertical component of the bullet's velocity is zero.

Also, by a flat parking lot i mean perfectly flat (planar).

Originally posted by davegage
Consider the following ballistics tests:

you are standing on a raft in the middle of the (perfectly calm) pacific ocean somewhere. you fire bullet A parallel to the water around you from shoulder height while at the same time you drop ...[text shortened]... lausible answers based on how picky you are with your assumptions.

Well, air effects like wind will affect this. This can go either way depending on how the wind is going. Friction won't affect the issue, unless one bullet has a different orientation than the other.

In addition, the curvature of the Earth will very slightly affect this. This factor will make the bullet you drop land first as the surface of the water will "drop away" from the bullet that was fired.

Maybe the disturbance of the water caused by shooting the gun might slightly affect things too.

The parking lot won't have the disturbed water effect, but the others will be the same - assuming a "flat" parking lot is actually conforming to the round shape of the Earth.

Overall though, except for these tiny factors, both hit at the same time.

EDIT - Oh yeah, forgot raft height.

Originally posted by davegage
I guess to be more clear, I mean that at the instant the bullet is fired, the vertical component of the bullet's velocity is zero.

Also, by a flat parking lot i mean perfectly flat (planar).

First to last to fall, IMHO:

1) Bullet shot at planar parking
2) Bullet dropped at parking and bullet dropped at boat (assuming height is the same)
3) Bullet shot in ocean.

They both hit at the same time.

Bullet A may be moving, but it will move in an arc, forward velocity and gravitational pull both acting on it.

Bullet B only has gravity acting on it, but the same amount as A.

Originally posted by Alcra
They both hit at the same time.

Bullet A may be moving, but it will move in an arc, forward velocity and gravitational pull both acting on it.

Bullet B only has gravity acting on it, but the same amount as A.

What about the curvature of the earth?

It is impossible for the bullet's trajectory to be parallel to the earth's surface as horizontal velocity is higher than vertical in at least part of the trajectory. So bullet A is fired in a slightly upward (considering height as measured on earth) trajectory.

I'm 6 feet tall. Will this make a difference?

Originally posted by davegage
Consider the following ballistics tests:

you are standing on a raft in the middle of the (perfectly calm) pacific ocean somewhere. you fire bullet A parallel to the water around you from shoulder height while at the same time you drop from your hand an identical bullet B from shoulder height. Which bullet hits the water first?

now suppose you run th ...[text shortened]... d?

i could forsee several plausible answers based on how picky you are with your assumptions.

The fired bullet will touch down later. Modern bullets aren't just lumps of metal, they're specifically designed to fly through the air like a javelin. This causes the bullet to experience a lot of air resistance to motion perpendicular to its axis of rotation, so it stays in the air longer (improving range and accuracy). On the other hand if you just drop a bullet, its central axis will point vertically, so it'll drop quite quickly. Also, the Earth's curvature will help slightly, as other people have said, but no rifle is powerful enough to send a bullet into orbit or anything like that.

I don't see what difference there is between the ocean test and the parking lot test.


Here's another bullet-themed puzzle:
An astronaut stranded on a desolate, airless planet plans to kill himself with a gun (which we'll assume is one which works in space) but can't bear to point the gun at himself. Instead, he carefully takes aim and fires the gun directly forward. The bullet travels at x m/s, and y seconds later, the bullet hits him in the back of the neck, at the same elevation as it was fired. Assuming the planet is spherical and of uniform density, what are the planet's radius and density?