# Three amigos

**Classical Mechanics**Level 4

Margo and Sven are outside in a field, standing right next to each other and talking. We'll put x,y coordinates on the field and measure everything in meters. Ursula, a friend of both Margo and Sven, is also outside walking due north (positive y-direction) at \(1~\mbox{m/s}\). When Ursula crosses the origin (at \(t=0\)) Margo and Sven (at coordinates \((100,0)\)) notice her and decide to walk over and say hello.

Margo knows a little physics, and so she figures out how she should walk at \(2~\mbox{m/s}\) to meet Ursula in the shortest amount of time. Sven doesn't know any physics, so he just always walks directly towards Ursula, also at \(2~\mbox{m/s}\), until he catches up to her.

If the time Sven meets Ursula is \(t_s\) and the time Margo meets Ursula is \(t_m\), what is \(t_s-t_m\) in seconds?

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