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?

Assume no air resistance or side wind, then the arrow will stay perfectly aimed at your midline throughout.  Also, since the arrow's launch velocity is perpendicular to the ground, gravity acts indepdendently.  The arrow will take 35m/60 m/s to reach you or 0.58333 sec.  In that time, it will drop by z= 0.5 * (accel grav=9.807 m/s/s) * (0.58333s)^2 or 1.669 m, and thefore be 1.75-1.669=.081m above the ground.  Therfore the arrow will  go between your legs, so long as your inseam is longer than the hypoteneuse of a right triangle with base .4m/2 and height .081m, or about 8.5 inches.  So, you will be OK unless you are a very small child or a very short midget.

 

Edited on July 14, 2006, 5:55 pm

Edited on July 14, 2006, 5:55 pm

Posted by Kenny M on 2006-07-14 17:52:08