2018 End-of-Fall Detroit Mercy Math Problem

Can you escape from the monster and reach the shelter?   You are stranded in the middle of a road in a vast desert, and there is a monster sitting somewhere out there on the road (you don't know in which direction), staring toward your location, waiting to eat any one it can see.

The monster's range of vision \(v\) (meters) is greater than your range of vision \(w\) (meters), and once the monster sees you, then you will instantly be eaten up (the monster can run with essentially infinite speed).

 Shelter      You             Monster
 ---X----------X-----------------X---

There is also a shelter on the road in the direction opposite to that of the monster (see diagram above), but you can't see the shelter, and you don't know in which direction it is. Luckily, the shelter is closer to you, by \(c\) (meters), than the monster. Also, you know the values of \(v\), \(w\), and \(c\).

Determine, with proof, a necessary and sufficient condition (on \(v\), \(w\), \(c\)) that guarantees that you can reach the shelter with a suitable strategy. Describe in detail your strategy to reach the shelter under this condition. (Assume \(v \gt 0\), \(w \gt 0\), \(c \gt 0\).)