# How does the height of a jump change if the body is scaled down?

This is a physics question that appeared in the movie 'The Internship.'

If you are reduced to the size of a coin and put into a blender what would you do?

Apparently the answer was that with a reduced size you could jump higher and jump out the blender.

I would think that if you are smaller your strength will also be smaller so you could only jump a few centimeters and could not escape from the blender.

So how does it work?

## 2 Answers

A rough idea is this. The strength of your muscles scales as the square of their radius (if you imagine them being like some tubes or something) and your weight scales with the radius squared times height or with the third power (assuming your density is constant during the shrinking process). Then the smaller size will result in less strength but also a lot less weight (second power beats third power when you decrease the size).

You could easily jump out of the blender.

The scale cancels out and you can jump the same absolute height. So if you can jump 30cm when you're 180cm tall, you can still jump 30cm when you're 18cm tall or 1.8cm tall or 18m tall.

See What's wrong with Arnold's scaling argument on jumping height? for derivation and (endless) discussion...