The Physics of Size: Could Mini-Me Jump as High as Full-Size Me?

Image: Rhett Allain. Normal Rhett, smaller Rhett, smallest Rhett

Sometimes I watch videos on YouTube. There was this fun Veritasium video with an interesting interview question from Google. It goes something like this.

You are shrunk down to the size of a nickel and put in a blender. How do you escape before the blender is turned on?

The answer is apparently that you just jump out. The idea is that a 5 centimeter tall person could jump just as high as a normal sized person. I mean, it sort of makes sense — there are many dogs that can jump as high as a horse, right?

Is this really a legit solution? Oh, let’s do it as a physics problem.

The Physics of Jumping

I’ve done this before, so here is my short version. I want to calculate the force (F) a person exerts on the floor in order to jump a height y. Let me start with the jump in three pictures. Squatting, end of jump, highest point. Here’s a diagram.

Of course with physics there are many ways to look at this problem. In this case, we are only dealing with changes in position and we don’t care about the time. This is a good hint that we…