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.is tangent to the pursuit curve . This tells us that where
(Your answer must involve the three variables , , and )