Monkey Bidness II

[Green Dragon]

If the hunter aim directly at the monkey's eyes, assuming this means that he sees no recoil from the gun, then the dart will fall to the ground before it reaches the monkey's vertical plane, and will not hit him, if the hunter is far enough away.

Also, you have to asssume that even if the hunter is on the same horozontalm plane as the monkey, and he shoots, then when he shoots, the dart falling at the same speed as the monkey will be a problem- remember, to fall, the monkey has to see the gun recoil, decide to let go, and then send the message to his hands to let go. This all takes time, but if he has enough time to do all this and avoid a normal shot, then the dart must be very slow or the distance between them very great, since the speed of thought and the speed of light are both very fast. If the monkey is in a tree of a normal height, the dart will very likely fall to the ground before it gets to the monkey.

If it dosen't fall to the ground first, then assuming that the distance between them is great, all the time it takes the monkey to do all this will keep the dart from leaving the gun at the same time as the monkey dropping; the monkey will fall a moment later, and the dart will go BELOW the monkey.

Other than doing something like getting below or above the monkey, then the only way for the hunter to get the little sucker is to compensate for all of this, a worthy task.

[Ghost Post]

First, to quote Wonko the Sane(I think), we must remember that this land of Puzzleania is inhabited with large-brained scientists with very little common sense.

Secondly:

As I mentioned before, according to the laws of physics, the rate of decrease in vertical "velocity" is affected by gravity at a constant rate. Therefore, even if the hunter aims from below or above the monkey, the rate of decrease in vertical velocity will be the same as the rate of decrease of vertical velocity in the monkey- therefore, the two will intersect.

The only real problem we have to solve with this scenario is the fletching of the dart. However, monkeys have air resistance too. If the hunter aims at the center of the monkey(ie), then the dart will hit him for sure.

If you have any questions, consult your local physics professor- it's a classic high-school physics problem.

Still stumped?

Try [u]The Cartoon Guide to Physics[/u] by Gonick and Huffman.

[Green Dragon]

I don't think that this is your classic physics problem RubberPaw- in the classic physics problem, the dart would leave the gun at the same instant as the monkey starts his fall.
My point is that the monkey has to see the light from the gun after it shot, think "I need to let go" send nueral signals to his hands to tell them to let go, and then he falls. In this case, the monkey starts his fall a little while after the dart leaves the gun. If the monkey is close to the hunter, or large at all, then that dosen't matter, but if the hunter is far away and the monkey is small, then the dart will not hit him unless the inital lift the dart gets from leaving the gun and the fact that the dart falls slower than the monkey compenates for that fact.

In all, I think this is a very complex puzzle if you try to solve it the normal way- if you try to, i think that you have to find the numerical values or assume instanious falls and no air resistance. If you don't and you don't have numbers, (which you don't) then i think you nail him in the upper cranium or the arse.

[HyToFry]

I'm sorry Green Dragon, but your wrong...

This is the grey labyrinth, EVERYTHING IS TAKEN AS ABSOLUTELY LITERAL HERE EVERYTHING NO EXCEPTIONS..

The Puzzle says:

[Ghost Post]

GreenDragon, this is great. The neural time(and btw, he doesn't look for flame. He looks for recoil) offsets the height problem caused by the fletching on the dart.(if you want to look at it that way. I don't. But oh well )

[Green Dragon]

I think that you are right. I tried to post something about that, but I'm new at this, and it somehow got lost. I think that even if you do not have a delay for him to think, then you still have a delay for the light from the recoil to the reach him. This takes almost no time, but the height gain from the fletching of the dart gains almost no height either, so I think that if anything, they cancel each other out to a degree, and I have no argument left, unless I want to argue that the monkey is about 1nm tall (five times the sixe of an atom,) and that it has to be exact. I won't do this because it really dosen't make any sense.

[schmyguy]

Now maybe I'm being to literal or I miss read the problem but why do we have to consider the dart's fletching?
The hunter should pretend to shoot (the monkey has made his deduction from visual input) then shoot horizontally. There is no fletching in the puzzle but more importantly the hunter should shoot where his instincts tell him to. If children can catch balls without understanding ballistics or calculus, the hunter should know where to shoot instinctively.
However, my final answer is the hunter should shoot himself in the face - shooting monkeys is not nice.

[ronl]

This may have been posted before (I do not have the patience or time to read through all the posts)... but shouldn't the hunter just position himself directly under the monkey?

Then, it does not matter how fast the dart is, what the trajectory is, how fast a monkey falls, etc. He would just need to be prepared for falling monkeys if he hits, or loaded darts if he misses.

[HyToFry]

I did say that before, i thought the same, makes sense to me..

trees are about "mere meters" right?

why the hell not

[Green Dragon]

oh, but putting himself directly under the monkey is to EASY- it makes sense, so why should he do it?

It does, work, and in my opinion, really is sensible, or the other alternative, standing above him (although I don't know how he gets up there.)

I think that brainaics like us just like to take the hard way out, so that's why we're ignoring thise two solutions and a few otheers that would make this particular hunter's life much easier

[This message has been edited by Green Dragon (edited 04-15-2000).]

[Roni]

I think we're making this too difficult. The answer is not that the hunter goes below the monkey and then shoots him, because the puzzle states simply that the hunter "changes his aim," not that he moved. Besides, the hunter shoots from "mere meters away." Here's the way I look at this.

For a hunter to hit a monkey that doesn't try to drop out of the way (which is what most monkeys in this riddle do), the hunter must aim above the monkey. This is because the dart will, under the influence of gravity, hit a point below a target sighted along the gun. Thus, most hunters aim a bit above a monkey's head and are able to hit the monkeys.

Our smart monkey figures out that if he drops away at the instant the gun fires, then the dart will fly up its parabolic path and hit the point where the monkey used to be--in this time the monkey has fallen a small distance below that point: the monkey is safe.

Since all objects fall at the same rate (this is a basic fact of classical mechanics--air resistance won't play much of a role for the monkey for obvious reasons, and it won't affect the dart because the dart is, I am assuming, fairly dense), the dart, when it gets to the point in its path lying on the vertical line along which the monkey falls, will be a certain distance below the target sighted along the gun. The monkey, falling at the same rate and beginning its fall at the time the gun was fired, falls exactly the same distance. Thus, to hit this cunning monkey, the hunter must aim the gun directly at the monkey. The monkey falls a distance x, and the dart arrives a distance x below the monkey's original position. Monkey brains for dinner.

I am certain about the physics of what I have reported here. If you don't believe me about aiming at the monkey's original place and still hitting it, work it out on paper--the calculations are relatively easy.

roni

[Mercuria]

one more case, though. if the monkey will fall to the ground before the dart reaches it, then the hunter must aim so that the dart will hit the ground directly under the monkey.

[Roni]

You're technically right. But the puzzle says the hunter is "mere meters" from the monkey, and I imagine the gun fires the dart at more than x m/s, where x is the largest number of meters you consider to be "mere."

[hank]

I've had a problem with this puzzle ever since it was first posted. Now that the solution has been posted, I am somewhat disappointed. The problem is the inclusion of the phrase "mere meters away". Intuitively, it suggests to me a distance of less than 10 meters, and thereby making any allowance for gravity irrelevant. A small bore rifle such as the 22 can easily fire a round at 300 m/s. Therefore it would take 1/30 seconds to travel 10 meters. The drop due to gravity over that small period of time (0.5gt^2) comes to 0.5 cm. or 1/8 of an inch. If the hunter is worried about that kind of accuracy, he had better have a scope and a tripod as well.

[This message has been edited by hank (edited 05-06-2000).]

[araya]

Woah, nice to see you again hank.

I had the same thoughts, although the hunter is said to be using a tranquilizer gun, which you do have to get pretty close with I think.

[Wonko the Sane]

Indeed. Tranq guns are very innacurate because the projectile spins just the same as a bullet does. To try and counteract the problems, they have feather flights to keep them on path. However, a tranq fun fires are far, far, far slower than 300 m/s. If it fired at a rate like that, the dart would hit the monkey, bore through it, and come out the other side, killing it. Obviously, tranq guns don't do this kind of damage because they aren't meant to be lethal. Also, the flights on the dart slow down it's spin faster, thus making it's actual flight less streamlined and slowing it down. I would say that even at a distance of under 10 meters, gravity would become a factor.