Let us consider the air with the index 1 and the lucite with index 2. Using the Snell's Secound Law, we have:
Entering the unknowns, remembering that the air refrective index is 1 and the lucite refrective index is 1.5, comes:
Using the arcsin properties, we get:

Obs: Approximate results, and the drawing is attached
If you notice any mistake in my english, let me know, because i am not native.
maximum speed of cheetah is

speed of gazelle is given as

Now the relative speed of Cheetah with respect to Gazelle


now the relative distance between Cheetah and Gazelle is given initially as "d"
now the time taken by Cheetah to catch the Gazelle is given as

so by rearranging the terms we can say


so above is the relation between all given variable