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A Trophy Hunter

Posted by Karl Sharman on October 5, 2010 – 9:58 am

In deepest, darkest, Africa, a hunter stalks a monkey. He wants to shoot him with his tranquilizer gun and take him back to America for display at the zoo. The monkey, on the other hand, wants to stay in the jungle and swing in the trees.

This particular monkey is more cunning than most. He’s observed that the hunter carries a big long stick which he points at other monkeys. When the stick jerks back, a split second later the monkey he was pointing at falls from the tree. In an amazing leap over the evolutionary chain, the cunning monkey has decided that something must be coming out of the long stick and knocking the other monkeys out. He reasons that if lets go of the tree branch he is hanging from as soon as he sees the stick jerk back, the hunter will miss and the monkey will escape.

And it works.

For days, whenever the hunter sees the monkey, he takes aim with his excellent marksmanship, fires, but the monkey drops out of the way.

Eventually the hunter figures out what’s going on. The next time he sees the monkey, a mere 10 meters away, he changes his aim, fires, and it’s bedtime for the monkey.

Where did the hunter point his gun?

This post is under “Tom” and has 27 respond so far.
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27 Responds so far- Add one»

  1. 1. Ana Said:

    He aimed his gun below the monkey so that when it saw the gun crack back and dropped itself down, the hunter still would hit because he aimed for where the monkey would be not where it was when he saw it.

  2. 2. Rantelvena Said:

    well it would seem he points under the monkey’s position, but then this wouldn’t be a question in TOM, thus I think it’s more likely he points the gun somewhere else… but not quite sure where yet… I’ll think of it a bit…

  3. 3. Chris Said:

    At the monkey.

    Previously, he would have been pointing higher to allow for the shell dropping under the influence of gravity. The shell and the monkey drop at the same (accelerating) rate.

    He may actually point a little higher to allow for the monkey’s reaction time.

  4. 4. John24 Said:

    At the same point as usual.

    Being mentally far superior to the inferior monkey, our hunter has come to the conclusion this monkey is no ordinary monkey and is smart enough to put 2 and 2 together. Our hunter has stalked this monkey until he has a clear shot from out of sight.

    He could aim low in the hopes his extremely slow bullet somehow takes enough time to get to the drop path of the monkey, but this smart monkey would soon understand this new method, if it fails, and start avoiding the new tragectory.

  5. 5. wamatt Said:

    When the stick jerks back, a split second later the monkey he was pointing at falls from the tree
    in 1 second the monkey falls 9.8 meters
    so all the hunter has to do is aim 9.8 meters below the monkey
    even if the hunter miss a couple time the monkey will not figure it out because it will look like all the other times he fired
    the angle the hunter needs to firer at depends on the the height of the monkey
    the higher the monkey the less accute the change of angle will need to be

  6. 6. slowlyslowly Said:

    right in the monkey’s ass, shooting directly from below..
    watch your steps and wear a hat against the monkey’s droppings..

  7. 7. joey Said:

    slightly above the waist. being ony ten meters away even a slow speed projectile would strike him only milli-second after the monkey drops(due to the reaction time of the monkey). therefore hiting the monkey dead on in the cheast the best place to put a tranqilizer dart in to a monkey(other than the rear end in which he woud have to aim at the monkeys knees)

  8. 8. Wendy Said:

    he shot at the way the monkey kept on ducking.

  9. 9. Paul H Said:

    I think the hunter is waiting for the monkey to fall asleep and then BANG! Well, it was bedtime for the monkey. :)

  10. 10. Saleena Sharp Said:

    The hunter would of had to hit the I guess the monkey should hurry up if he wants to make his flight!! lol

  11. 11. Cathrine Said:

    10 Meters under the monkey.

  12. 12. BMJ Said:

    well, you could do some calculations including velocity of the dart, gravity, the 10 m distance, variables due to any wind, and the reaction time of the monkey, but I think its not necessary. he aimed a little lower than what he had been aiming at, shooting where the monkey will be rather than where it is. duh.

  13. 13. Karys Said:

    On the branch. Since you say the monkey “lets go of the branch” that means he is falling UNDER that branch. Therefore by hitting the branch at the right spot, it should fall on the monkey and presumably stun/trap/kill him because that monkey believes there is no danger in the moment after the hunter fires, since he has to reload… (if it’s a machine gun he uses, that’s another problem…)

  14. 14. Karl Sharman Said:

    Chris, the professional Monkey Assassin gets this monkey of his back first.

    Where did the hunter point his gun? Straight at the monkey.

    Previously, the hunter, being a skilled marksman had trained through years of practice to always set his sites above the target. Why? Because bullets are influenced by gravity. In the absence of gravity, shooting would be much easier. You could always point straight at the target no matter how far away it is, the bullet would fly straight at it. But with gravity, the bullet’s trajectory is a semi-ellipse. When the monkey started to drop as soon as the gun was fired, the hunter just needed to abandon his training, because now the monkey and the bullet were both in free fall. Since gravity acted on both equally, they fell at the same rate.

  15. 15. Chris Said:

    Karl, the shell’s path is a parabola.

    All the same, the shell would have to be very slow or fired from a long distance.

  16. 16. Karl Sharman Said:

    Chris, you might need to help me on this definition thing…
    Parabola Definition: Any point on a parabola is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix)
    If the focus is the point where the monkey is hit by the dart and the directrix is the line of sight where the bullet would go without the effects of gravity, the parabola being the actual trajectory of the dart, then it can’t be a parabola, by definition, can it? Or am I misinterpreting the “focus” part of the definition?
    I assumed that it was an ellipse due to the acceleration of gravity, and that in 10 mtrs travel, the terminal velocity would not be attained by the bullet.
    I’ve read this back to myself, now that I’ve written it, and it doesn’t seem to convey my meaning very well, but that is due to alcohol poisoning that I am still recovering from since last night.

  17. 17. Chris Said:

    Hi Karl. An ellipse is e.g. (x/a)² + (y/b)² = 1 and is a closed path. A parabola is e.g. y = ax² and is open. If x is horizontal distance, then we’ll have x = vt for a constant speed. Due to gravity, y will vary as t²; hence, etc.

    However, thinking about orbits, I realise that the path must be part of an ellipse; but that isn’t what the textbooks will say.

    The monkey cannot be at a focus, as the focii are inside the ellipse. e.g. the Sun is at one focus of the ellipses that describe the orbits of the planets (assuming the Sun to be of virtually infinite mass).

    See the Wiki:

    PS Thank you for putting up some good problems recently. I just wish that I had more time to look at them properly.

  18. 18. neehar Said:

    Since the monkey ‘falls off the tree’, he would point to the ‘hanging tail’ of the monkey.

  19. 19. MONIL Said:

    at himself

  20. 20. Karl Sharman Said:

    Ah, I see, I had forced the focus to be on the ellipse, rather than inside.


  21. 21. Kevin Said:

    at the monkey’s stomach

  22. 22. Chris Said:

    Hi Karl. In the case of your problem, the focus of interest is at the centre of the Earth (nowhere near the monkey ;) )

    You may not know that one way of pumping a ruby laser involves placing a xenon flash tube at one focus and a ruby rod at the other. Nearly all the light from the xenon flash arrives at the ruby rod; it travels the same distance and so arrives at the same time too. Very sweet.

    One way of drawing an ellipse involves placing two pins in a board (at the focii) placing a loop of string around them, and moving a pencil in such a way that the string is kept taut. Hence the laser trick.

  23. 23. tas Said:

    i think he pointed it to himself.. it would have confused the monkey. The monkey would have thought the man would die. And then he can take the monkey by surprise and shoot him!

    btw, how we find out what the actual ans is?

  24. 24. sean Said:

    he aims low and in a sense ambushes the intended target in the position he will be after the shot is fired not in the position at which the target was aquired

  25. 25. guest Said:

    He point his gun at the monkey but he changes his aim, fires, and it’s bedtime for the monkey.

  26. 26. cazayoux Said:

    Why doesn’t he aim near (just above) the ground where the monkey will land?

  27. 27. Ultra Man! Said:

    Why can’t he just sneak up on the monkey and shoot straight at it before the monkey realizes that he needs to avoid the dart?

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