# Heron's Problem and Snell's Law

Use calculus (and a CAS if needed) to compute the value of the $x$ coordinate of the point $C$ on the $x$ axis that minimizes the time of travel along $A\to C\to B$ with $A=(1,3)$, $B=(4,-2)$, $v_1=4$, and $v_2=5$. Enter your solution into the input box below to verify that the value of $\frac{\sin \theta_1}{\sin \theta_2}$ is as predicted by Snell's Law.