Crossbow Challenge
Science brain teasers require understanding of the physical or biological world and the laws that govern it.
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).
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Comments
chloe31
Jun 15, 2003
| takes a lot of working out but is good |
whyme 
Jun 15, 2003
| i would any way cause im not that tall!  |
tissue  
Jun 17, 2003
| Lol, I'd be scared to death! |
wolfen
Aug 10, 2003
| 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.
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xiaobaby
Sep 09, 2003
| 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 |
curtiss82 
Dec 24, 2003
| 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. |
(user deleted)
Apr 02, 2004
| this is great. took some time for me to solve it.
you think $1000 is enough for the scare?  |
Sunrose
Aug 28, 2005
| very good teaser and well written  |
kibber
Sep 19, 2005
| 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) |
Jerrythellama
May 22, 2006
| Thats a slow bolt |
Jerrythellama
May 22, 2006
| btw, crossbow arrows are bolts |
Jerrythellama
May 22, 2006
| whupps. nm about the speed =D |
Vudluxi 
Jun 03, 2006
| 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. |
Nymphadora313
Dec 05, 2009
| It was a good teaser..It was easy for me though -I bow hunt, so I just knew ... |
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