söndag 16 februari 2020

Theoretical Pole Vault Limit for Duplantis?



Duplantis says that $6.30$ is not impossible. What does theory say? Inertial energy is $m\times \frac{v^2}{2}$ with $m$ mass in $kg$ and $v$ speed in $\frac{m}{s}$, and potential energy is $m\times g\times H$, where $g =9.81\,\frac{m}{s^2}$ is gravitational constant and $H$ is height in $m$.  

Duplantis horisontal speed is 10 which gives an inertial energy of $m\times 10^2/2$, which if completely converted into potential energy corresponds to $H=5$. This requires the pole to be fully elastic as well as the ground support for the pole. Duplantis uses a very stiff pole and so may reach the height 5.00 from the pole alone. The remaining height must come from the arms. Since the limit of high jump using the legs is about 2 $m$, it is apparently possible to reach 1.18 $m$ with the arms alone.

Another way is to recall that a human being can develop 1 hp momentarily and thus lift 75 $kg$ 1 $m$ during 1 $s$. So 2 $m$ may be impossible, and thus 7.00 $m$ may be the theoretical limit? 


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