Brain Teasers
Crossbow Challenge
An expert marksmen crossbow hunter, who has never missed a bullseye in his life, has his crossbow mounted on a stand with the shaft of the arrow 175 centimeters (about 5 feet 9 inches) above the ground; with the shaft of the arrow perfectly parallel to the ground. The hunter offers you $1000.00 to stand 35 meters away from the tip of the arrow to act as his target. The rules of his challenge state in order to win the money as his target you have to stand perfectly still, stand tall with your feet 40 centimeters apart, and you can not move in any way until either the arrow hits you or passes by you. When you get the designated distance away from the tip of the arrow the hunter will aim the arrow directly at the vertical mid-line of your body (medial sagittal plane), without changing the arrow's height or parallel. He will pull the trigger firing the bolt toward you at an initial velocity of 60 meters per second. Do you take the challenge from the hunter?
Answer
Yes you do.The arrow is 35 meters away and is fired at 60 meters per second. It will take the arrow 0.58333 seconds to reach you
(35m 60 m/s = 0.5833 seconds). Gravity pulls the arrow down at the rate of 9.8 meters/second/second. You can calculate the distance an object falls due to gravity after a certain amount of time by the formula 1/2*(the rate of gravity)*time falling*time falling or 1/2gt^2 . As soon as the arrow is fired, gravity will start to pull down the arrow, so as the arrow gets closer to you it gets closer to the ground. After 0.5833 seconds, the tip of the arrow would have fallen 1/2*9.8*0.5833*0.5833 = 1.667 meters or 166.7 centimeters. The tip of the arrow will be about 9 centimeters above the ground when it reaches you, just low enough to go through your legs between your ankles (assuming that your legs at 40 cm apart are not touching at the ankles).
Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
takes a lot of working out but is good
i would any way cause im not that tall!
Lol, I'd be scared to death!
I hate to be a wet blanket on this but you'd be a fool to take that bet. while the math may be perfect theres too many other factors to be added in. If the fletching is off in anyway it will effect the flight of the bolt (left,right, or even up).
if your outdoors you have windage and ground elevation to take into account. this is one of those things that looks good on paper but don't bet your life on it. theres to many variables.
if your outdoors you have windage and ground elevation to take into account. this is one of those things that looks good on paper but don't bet your life on it. theres to many variables.
i agree to wolfen. also,(just to be a little idiotic) $1000 isnt really that much... anyway, this is a tough one needing much thinking
This is a great physics problem. Not that many people would have thought about the distance the arrow would have fallen by the time it reaches its target.
Apr 02, 2004
this is great. took some time for me to solve it.
you think $1000 is enough for the scare?
you think $1000 is enough for the scare?
very good teaser and well written
this is a terrible teaser. and curtiss thinks he's the only one in the world who's heard of gravity...smart guy he is. (BTW i don't like curtiss-you should read all the funny things i write about him)
Thats a slow bolt
btw, crossbow arrows are bolts
whupps. nm about the speed =D
Good maths teaser, but I didn't sit there and calculate it. It just felt right that the arrow parallel to the floor wasn't going to carry.
It was a good teaser..It was easy for me though -I bow hunt, so I just knew ...
Presumably inspired by the story of William Tell, who had to shoot an apple off his son's head.
The solution assumes that there is no wind, which perhaps should be specified. Also it ignores air resistance, but that doesn't matter because (if it made any significant difference) air resistance would cause the bolt to fall further, making the margin of safety larger.
Alternatively I suppose it could be set on the moon, with appropriately adjusted measurements.
The solution assumes that there is no wind, which perhaps should be specified. Also it ignores air resistance, but that doesn't matter because (if it made any significant difference) air resistance would cause the bolt to fall further, making the margin of safety larger.
Alternatively I suppose it could be set on the moon, with appropriately adjusted measurements.
To post a comment, please create an account and sign in.
Follow Braingle!