As you watch high jumpers sail over the bar this summer at the London Olympic Games, keep this equation in mind: U2 = 2gH. It explains why most of jumpers do the backward flip known as the Fosbury Flop. As University of Cambridge mathematician John Barrow writes in his book Mathletics: A Scientist Explains 100 Amazing Things about the World of Sports (W. W. Norton, 2012), the Fosbury Flop keeps one’s center of gravity low to the ground, and the lower one’s center of gravity, the less energy is required to successfully jump over the bar. In the above equation, U is the speed of the jumper (and thus the energy required), g is the acceleration caused by gravity, and H is the height of the center of gravity. Surprisingly, it is possible for the high jumper’s body to fly over the bar while his or her center of gravity passes below it.

Now, you might ask, why do many of the jumpers leap backward? That part is easy: when your back is to the pole, there is less chance that your arms or legs will hit the bar and knock it down.

COMMENT AT ScientificAmerican.com/aug2012

2 Comments

1. 1. optohawk 10:52 AM 7/29/12

   To be more precise, the speed U of the jumper is not the same as the energy of the jump. Rather, the energy is equal to one half times the jumper's mass times the square of the speed U.

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2. 2. mikegonzalez2k 09:59 PM 8/2/12

   Here is the actual equation, its from the conservation of energy
   
   KE = PE
   ½mv² = mgh
   ½ v² = gh
   v² = 2 gh
   
   Thus the square of an object's velocity is equal to twice the product of the acceleration of gravity and the height. This is simple high school physics.

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