Written by Colin+ in ask uncle colin.

“What are *you* doing here?”

“Never mind that, sensei, how on *earth* did they catch you?”

“… I don’t want to talk about it. In any case, I was only doing 5% more than the speed of light.”

“Yeah, that poses more questions than it answers, in honesty.”

The Powerpoint slide had the car coming to a stop from 30mph just in time to avoid hitting Tommy, the six-year-old chasing his ball into the road.

“Now,” said the instructor, “what if you’d been doing 32 instead? How fast would you hit Tommy?”

The dozen or so people on the driving awareness course muttered a bit. “Two” was a common answer. “32”, said someone who clearly wasn’t listening.

“Eleven,” said the Mathematical Ninja, confidently. “11.136 or so.”

The instructor raised her eyebrows and asked how he’d come up with that. She really didn’t realise what she was getting into.

“Kinetic energy, square law, yadda yadda yadda. $v^2=u^2 – 2as$, if that’s your cup of tea. In any case, the final speed here is the square root of $32^2 – 30^2$.”

“… I really don’t see how that…” Luckily, the instructor was a police officer and the Mathematical Ninja figured that one lot of trouble was enough for today^{1}.

“$32^2 – 30^2$ is $62 \times 2$, by difference of two squares, or 124. That’s a smidge more than $11^2$, and the error is about $\frac{3}{22}$. That’s $\frac{14}{22} – \frac{11}{22}$, which is 0.63 recurring less a half, making 0.136. Give or take.”

The instructor tried very hard not to make a face, and moved on to the next slide without any further comment.

The Mathematical Ninja, meanwhile, looked to camera and sternly advised readers to watch their speed.

- While the Mathematical Ninja respects regular law enforcement, they have no such qualms about the physics police since they became a freemeson. [↩]

## Donald Cram

3/22 was calculated on another post from this site: http://www.flyingcoloursmaths.co.uk/mathematical-ninja-twenty-sixths/

Number has an excellent video that shows how this calculation comes about in a visual manner: https://www.youtube.com/watch?v=i3D7XYQExt0

(Edit: Took the liberty of fixing a typo).

## Colin

Thanks, GM!