on the 
-axis, spots a pigeon at 
on the 
-axis.
Suppose that the pigeon flies at a constant speed of 50 ft/sec in
the direction of the 
-axis (oblivious to the hawk), while
the hawk flies at a constant speed of 60 ft/sec, always in the
direction of the pigeon.
The problem is to find an equation for the flight path of the hawk (the curve of pursuit) and to find the time and place where the hawk will catch the pigeon. Assume that in this problem all distances are measured in feet and all times measured in seconds. Leave out all dimensions from your answers.
Consider the diagram above (click on it for a better view)
which represents the situation at an arbitrary
time 
during the pursuit. The points 
and 
represent
the positions of the hawk and pigeon respectively at that time instant
, with 
representing the flight path of the hawk.
The pigeon's position 
is given by the following function of time
=
is tangent to the pursuit curve 
.
This tells us that 
where
=?????(Your answer must involve the three variables
, 
, and 
)
