Brain teaser

[arboldt]

(if achris will allow me)

Since this is iboats, the setting will be on a perfectly calm sea.

A rifle is loaded and aimed perfectly horizontal. Next to the muzzle is a slug of identical mass and shape as the rifle slug. At the same time as the rifle slug exits the muzzle, the other slug is dropped. (Now assume that it's rigged so the stated conditions actually happen). Which one hits the surface first?

This is a common question in a lot of physics classes, but I firmly believe the common answer is wrong. Why?

(Qualitative answers are ok, but this can also be quantified)

 

[Windykid]

Re: Brain teaser

Because of the curvature of the earth the fired bullet hits the surface first.

 

[Bass Man Bruce]

Re: Brain teaser

They hit at the same time.

 

[i386]

Re: Brain teaser

They are both falling objects. Both accelerate toward the earth at 9.8 meters per second per second. Since the earth is curved, the fired bullet has to fall further. The dropped one hits first.

If you could construct a perfectly level firing range with a length greater than the maximum distance the bullet will travel, they should hit the "ground" at the same time.

 

[bassboy1]

Re: Brain teaser

If you could construct a perfectly level firing range with a length greater than the maximum distance the bullet will travel, they should hit the "ground" at the same time.

Now the only problem here is, a flat range on the spherical earth isn't going to work properly. The gravitational pull of the earth is minutely smaller as you get farther from the exact center. Obviously, putting a flat range on the round earth, in some places, the gravitational pull would be different.

 

[JB]

Re: Brain teaser

What i386 said.

Had a similar question on a fizix exam (that I aced).

 

[angus63]

Re: Brain teaser

Depends on the velocity of the round and the height off the ground. If it's fast enough and high enough, it will continue into space without ever touching the earth. If it's a common round near the ground, than I'm with JB and i386.

 

[Caveman Charlie]

Re: Brain teaser

Um.... Since they both fall at the same speed. Wouldn't the fired bullet start falling as soon as it leaves the barrel? If so, then they would hit the ground at the same time.

 

[Bob_VT]

Re: Brain teaser

The one dropped along side will strike the ground first.

The bullet has left the barrel with energy moving it forward. One the forward energy is diminished .... it will start to fall at the same rate.

As an example a 45 apc slug shot straight up will travel about 2 miles while a 300 Win will go about 4 miles..... more energy.... longer flight time.

 

[i386]

Re: Brain teaser

One the forward energy is diminished .... it will start to fall at the same rate.

Nosir.... The moving projectile is not excused from the laws of physics above a certain velocity. It will begin to fall as soon as it leaves the barrel and at the exact same rate as the one dropped.

At least that's how it works down here in Georgia.

Disclaimer: Introductory physics explains ballistic trajectory as a parabola because the examples are worked out on a grid coordinate system. If you want to think of a fired bullet as an object in orbit (albeit an abbreviated one), the path is actually eliptical.

 

[angus63]

Re: Brain teaser

Bob
Fired horizontal at the same time, they would hit the ground at the same time, but the one with greater velocity would of travelled further. The force of gravity acts the same on all objects the same distance from the center of the earth. If Nolan Ryan and I threw baseballs horizontal, they would hit the ground at the same time;however, I could walk to pick my ball up and Nolan would hail a cab!

 

[arboldt]

Re: Brain teaser

They are both falling objects. Both accelerate toward the earth at 9.8 meters per second per second. Since the earth is curved, the fired bullet has to fall further. The dropped one hits first.

If you could construct a perfectly level firing range with a length greater than the maximum distance the bullet will travel, they should hit the "ground" at the same time.

Correct. Both fall at the same rate; both cover the same vertical distance at the same time, so the muzzle velocity doesn't affect the rate of fall.

However, because it is moving on a tangent to the earth's surface, the fired bullet has a slightly longer distance to fall. We don't know the horizontal distance it would go, but assume a long rifle shot could could travel 1 mile. The radius of the earth (from center to surface) averages 3956.5 miles. You can diagram this as a right triangle:

a = distance of bullet just before it's dropped to center of earth= 3956.5 miles
b = horizontal distance of fired bullet = 1 mile
c = hypotenese from center of earth to end of fired bullet's tangent

Solve for c: a^2 + b^2 = c^2 (remember basic geometry?)
(3956.5)^2 + (1)^2 = (3956.500126)^2

The difference between a and c is .000126 miles, or about 8 inches.

So the fired bullet actually has abut 8" further to fall.

 

[gnrboyd]

Re: Brain teaser

I'm glad you scientists and physicists got that all worked out. I had been up nights worrying about this very problem. Now I can add this bit of trivia to my temporary memory bank which expires when my head hits the pillow.

Now... on to another problem...... if I forget to put my plug in the boat before launching, how much time do I have to pull the boat back out of the lake before my boat sinks? I bet we'd have more real experimental data on this one and less theory.

 

[MikDee]

Re: Brain teaser

I'm glad you scientists and physicists got that all worked out. I had been up nights worrying about this very problem. Now I can add this bit of trivia to my temporary memory bank which expires when my head hits the pillow.

Now... on to another problem...... if I forget to put my plug in the boat before launching, how much time do I have to pull the boat back out of the lake before my boat sinks? I bet we'd have more real experimental data on this one and less theory.

That depends gnr, if it's rush hour at the ramp, forget it, your boat will sink, before you can get to it!

 

[Windykid]

Re: Brain teaser

Now... on to another problem...... if I forget to put my plug in the boat before launching, how much time do I have to pull the boat back out of the lake before my boat sinks? I bet we'd have more real experimental data on this one and less theory.

If you were operating a Boston Whaler it wouldn't sink at all.

 

[Coors]

Re: Brain teaser

If your boat is in the backyard, un-covered, with the plug in it, and it rains 2" in one hour, and your are one hour away, when is your starter under bilge water, and toast?




Answer-45 minutes

 

[Coors]

Re: Brain teaser

And I seem to remember, that the fired bullet, when first leaving the barrel, falls a little, and then rises more above the fired axis path, giving it more air born time than the dropped one.

 

[gnrboyd]

Re: Brain teaser

JB....

Had a similar question on a fizix exam (that I aced).

So....how did you do on the spelling exam?

 

[Caveman Charlie]

Re: Brain teaser

And I seem to remember, that the fired bullet, when first leaving the barrel, falls a little, and then rises more above the fired axis path, giving it more air born time than the dropped one.

Not according to some other people I talked to. They said that is only true if the rifle is sighted on a target. If it's just pointing parallel to the ground the bullet does not do that.

 

[i386]

Re: Brain teaser

Not according to some other people I talked to. They said that is only true if the rifle is sighted on a target. If it's just pointing parallel to the ground the bullet does not do that.

Sort of...

When sighting in a rifle you're setting it up to fire above the line of sight. When fired, the bullet is fired slightly upward and then falls some. Where the bullet's path intersects the line of sight is the distance you sited the rifle in at.