Puzzle Description:

The monkey and the hunter.

#1: Brian Bellis (mootpoint) on Dec 11, 2017 [SPOILER]

The set up for this problem goes something like this. A hunter aims directly at a monkey in a distant tree. The instant the gun is fired, the monkey drops. Does the monkey live or die?

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Perhaps I'm completely missing the point, but there are so many factors. First, did the monkey drop because he was already planning on falling and let go right before the hunter shot, or did he fall because he was hit by the bullet and couldn't hold on anymore? Second, if it is the first scenario, how far was the fall? If it was not a fatal distance from the tree branch to the ground, he is fine. If the second scenario is true, then it depends on whether the monkey was shot in a lethal place, i.e. the jugular, the heart, the brain... or did he get hit in the arm, leg, some other place that is not an instant kill?

Is there a simple answer that I am not seeing?

When I Googled the problem the example they used was a blow gun, which made the explanation easier to understand. But I am assuming that when you say gun, you mean a rifle as a shotgun wouldn't make much sense. Wouldn't the tremendous difference in speed between a bullet and a dart change things a bit? Unless it's a sniper firing from a mile or more away, if your aim is right with a rifle, you pretty much have one dead monkey an instant after the trigger is pulled and the discussion about the effects of gravity on falling objects wouldn't apply.

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A blow dart averages 400 ft per second compared to the average rate of a bullet of 2,500 feet per second.

From a large distance away, every hunter knows to aim above the target (except this guy). The monkey drops at the exact moment the gun fires. Both bullet and monkey and under the influence of gravity and fall the same distance in the same time. The monkey is no more. No actual monkeys were harmed during these physics demonstrations.
https://www.youtube.com/watch?v=0jGZnMf3rPo
https://www.youtube.com/watch?v=TbWiMsfr_DQ

Yes, but Brian, the way gravity pulls on the monkey, and the way gravity pulls on the bullet are different aren't they, since the bullet is actually a vector, right? It has been a long, long time since I've solved these types of problems (but I was pretty good at it at the time lol)...so I'm not quite sure of the terminology anymore. Help me out!

No, gravity pulls the bullet down from its straight line path at the same rate as the monkey. The only thing that messes with this is if the spinning bullet gets some lift and flies.

Hmmmm...I believe you, but can't quite wrap my head around why a force propelling an object forward wouldn't have any effect on the rate at which it drops (from gravity) compared to an object that just drops (from gravity)....

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Found to be solvable with moderate lookahead by infrapinklizzard.

A bullet that is shot horizontally will hit the ground at the same time as a bullet dropped right next to it -- just a lot farther away. Gravity is pulling the same amount on both of them. (In fact, gravity pulls the same amount on everything and to the acceleration due to gravity is a constant.) Since both bullets start at the same height and they both accelerate towards the ground at the same rate, they will hit at the same time.

Now apply that to the monkey. The monkey is accelerated at the same rate as the bullet. If the bullet is aimed directly at the monkey and the monkey lets go at the same instant that the bullet is fired, they will both accelerate toward the ground at the same rate, and so the bullet will hit the monkey.

Here is a video of a hammer and a feather accelerating at the same rate because there is no air friction to slow either down: https://www.youtube.com/watch?v=KDp1tiUsZw8

Now, it makes intuitive sense to think that heavy things drop faster than light things, but we've known since Galileo's time that they drop at the same speed (barring air resistance). Why? Gravity is obviously pulling the heavy one harder, but they accelerate the same?!? The answer is inertia. The heavy one is being held back more by inertia the exact amount that it is being pulled harder by gravity. https://www.youtube.com/watch?v=aRhkQTQxm4w

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Not exactly on-topic, but here's an interesting video on the very nature of gravity. Is it actually a force like the electromagnetic, strong nuclear, or weak nuclear forces? Or is it in fact just a result of the shape of space-time?
https://www.youtube.com/watch?v=Xc4xYacTu-E

Thanks, Brian and Joe. It finally sank in!

My high school physics teacher actually demonstrated this using an air rifle and a teddy bear. But he had the gun aiming straight across the room from the bear. This picture shows the gun aiming up at the monkey, and surely that would throw off the whole thing.

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