(Explanation by ID) Light travels from … to … in time …

These problems resolve the speed of light paradox in Example 9.

(Explanation by ID) Light travels from $A$ to $B$ in time $z/c$, distance over speed. Its arrival time is $t=\theta /2\pi +z/c$ so ${\theta }^{\prime }/2\pi =1-z^{\prime }/c$. Then $z^{\prime }=y^{\prime }\sin \theta$ and $y^{\prime }=100{\sec }^2\theta {\theta }^{\prime }$ (all these are ID) lead to
$y^{\prime }=200\pi c/(c{\cos }^2\theta +200\pi \sin \theta )$

This exercise builds on another exercise in its source book, which isn't shown here.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §4.2 Implicit Differentiation and Related Rates, #18