Question

An air traffic controller spots two planes at the same altitude flying toward each other. their flight paths form a right angle at point p. one plane is 150 miles from point p and is moving at 450 miles per hour. the other plane is 200 miles from point p and is moving at 450 miles per hour. 100 100 200 200 distance (in miles) distance (in miles) y s x p write the distance s between the planes as a function of time t.

Answer 1

Let the units of the problem be miles and hours. The first plane's distance from point p can be described by

... x = 150 -450t

The second plane's distance from point p can be described by

... y = 200 -450t

Since their flight paths are at right angles, the Pythagorean theorem can be used to describe the distance between them (s).

... s² = x² + y²

... s² = (150 -450t)² + (200 -450t)² = 22500 -135000t +202500t² +40000 -180000t +202500t²

... s² = 40500t² -315000t +62500 = 2500(162t² -126t +25)

... s = 50√(162t² -126t +25)