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 travelled 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) .