Crossbow ChallengeScience 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?
AnswerYes 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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