Question

You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 125 km south and 135 km east. Mt. Rainier is located approximately 56 km east and 40 km south of JBLM. If you are flying at a constant speed of 800 km/hr, how long after you depart JBLM will you be the closest to Mt. Rainier?
Convert hours into minutes in the final solution.

Answer 1

Answer:

  5.12 minutes ≈ 5 minutes 7.2 seconds

Step-by-step explanation:

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:

$(1256\sqrt{\dfrac{2}{677}}\,km)\times \dfrac{60\,min}{800\,km}=94.2\sqrt{\dfrac{2}{677}}\,min\approx 5.120019\,min$

5.12 minutes after departing JBLM you will be closest to Mt. Rainier.

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The attached graph shows the geometry of the problem.