Applied Optimization: Videos & Practice Problems

An ant needs to cross a garden to reach a sugar cube. The first part of the garden is covered in sand, where the ant moves at $2\text{ cm/s}$, and the second part is a patch of grass, where the ant's speed decreases to $1\text{ cm/s}$. To minimize the travel time, what should be the ratio of the sine of the angle at which the ant enters the grass, ${\theta }_1$, to the sine of the angle at which it moves through the grass, ${\theta }_2$?