5.12 minutes ≈ 5 minutes 7.2 seconds
What is Distance?
Distance. The length along a line or line segment between two points on the line or line segment.
Here, The flight path of the airplane is along the line ...
y = -125/135x = -25/27x
The perpendicular line through Mt. Rainier's location is ...
y = 27/25(x -56) -40
In standard form, these two equations are ...
25x +27y = 0
27x -25y = 2512
The point of closest approach has the coordinates that are the solution to these two equations:
(x, y) = (33912/677, 31400/677)
The distance d from the origin to this point is given by the Pythagorean theorem (distance formula) as ...
d = 1256√(2/677) . . . . . km
This distance can be converted to time using the speed of the airplane:
1256√(2/677) X 60/800 = 94.2√(2/677) ≈ 5.120019 mins
Thus, 5.12 minutes after departing JBLM you will be closest to Mt. Rainier.
The attached graph shows the geometry of the problem.
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