An airplane is flying at a speed of  mi/h.

At time , an altitude of  mi/h and passes directly over the radar station.

(a)

Find .

Observe the figure.

At , the distance between the airplane and the radar station is  mi/h.

The speed of the airplane is  mi/h.

Speed-distance relation:

.

.

Therefore .

The horizontal distance function is .

(b)

Find .

Observe the figure.

At time ,  is the distance between the plane and the radar station.

At , the distance between the airplane and the radar station is  mi/h.

 is the horizontal distance traveled by the airplane.

From Pythagorean theorem,

The function of distance traveled by the airplane at time  is 

.

(c)

Find the composite function  as the function of .

Consider the composite function .

                                               ( Since  )

.

(a)The horizontal distance function is .

(b) .

(c) .