newtonian mechanics - Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result.

The riddle goes as follows:

"imagine you are shrunk to the size of a coin (i.e. you are, say, scaled down by two orders of magnitude) but your density remains the same. You are put into a blender of hight 20 cm. The blender will start working in 60 seconds, what to you do?"

One of the best answers is apparently:

"I jump out of the blender to escape (yes the blender is still open luckily)."

This seems ultra non-intuitive to me and I have tried to find flaws in this answer but it seems to be fairly robust.

There are two ways you can think of it:

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  the mass scales as $\sim \: L^3$ and therefore it will be $10^6$ times smaller. If we imagine that the takeoff velocity $v_{toff}$ is the same as before being rescaled $v_{big}$. We get then the hight at which a mini us can jump by equating the takeoff kinetic energy and the potential energy i.e. $mv_{toff}^2/2=mgh $ $\Rightarrow$ $h_{mini} = v^2_{big}/(2g) = h_{big} \sim 20 \rm cm$

  
  


• 
  

  The second way to see it is to look more in details on how the power produced by muscles scales with the size of muscles. Basically, the power scales with the cross section of the muscle i.e. with the number of parallel "strings" pulling on the joints to contract the muscle. This implies that $P_{mini}=P_{big}/\alpha^2$ ($\alpha$ being the factor bigger than 1 by which you have been rescaled). We know that the takeoff kinetic energy will be given by $P \Delta t$. We assume now that $\Delta t \sim L/v_{big}$ so that $\Delta t_{mini} = L/(\alpha v_{big})$. In the end, this calculation tells us that $E_{mini} \sim E_{big}/\alpha^3$. However, equating again with the potential energy to get the hight we have $h_{mini} \sim E_{mini}/(m_{mini}g) = (E_{big}/\alpha^3)/(gm_{big}/\alpha^3)=E_{big}/(m_{big}g) = h_{big} \sim 20\:\rm cm$

  
  
  

These two reasonings seem fair enough and yet I don't trust the result they lead to. I would like to know if I am experiencing pure denial because of my prejudices or if there is some kind of flaw in the reasonings above (e.g. the fact that it is always assumed that the speed is unchanged when changing scale).

I also know that some tiny animals can jump more or less as high as human beings but it seems that most of the time these species have to use some kind of "trick" to store elastic energy in their body so as to generate enough kinetic energy at the takeoff to effectively jump super high.

If anyone has any thought on this, that would be very much welcome.