Suppose that a hawk, whose initial position is (a,0)=(3000,0) on the x-axis, spots a pigeon at (0,-2000) on the y-axis. Suppose that the pigeon flies at a constant speed of 50 ft/sec in the direction of the y-axis (oblivious to the hawk), while the hawk flies at a constant speed of 90 ft/sec, always in the direction of the pigeon.
The fact that the hawk is always headed in the direction of the pigeon means that the line PQ is tangent to the pursuit curve y=f(x). This tells us that (dy/dx)=h(x,y,t) where h(x,y,t) = ?
The pigeon's position Q=(0,g(t)) where i found g(t) = -2000 + 50t.
Could I then say something like the hawk's position P = ( j(t), k(t) ) where
j(t) = 3000 - 90t and k(t) = 90t
(Based on the starting position of the hawk on the x-axis)?
If I can do that, I'm not seeing how to get from here to the equation for h(x,y,t) that involves all three of those variables. Any tips/hints/suggestions?