# Puzzle #9 – Platformulae

Here’s a little mechanics problem that popped into my head one night.

Suppose you are standing on a platform. It moves horizontally back and forth in a sinusoidal way, so that its position $\bold{r}$ goes like

$\bold{r}(t)=(\sin\omega t)\bold{i} + 0\bold{j}$

You suddenly feel compelled to jump from the platform. To constrain the problem a bit, suppose that, in the instantaneous rest frame of the platform, you launch yourself at velocity

$\bold{v}=v_0(\bold{i} + \bold{j})$

that is, if the platform were stationary, you would jump at $45^\circ$.

The question is: when do you jump such that you travel the greatest horizontal distance from the origin? Do you jump off immediately, when the platform is travelling fastest, or do you jump off when the platform has stopped, since it has already carried you some distance? Or is the answer intermediate?

I like this problem because it tests your physical intuition, and has a tidy answer.