Question

You're flying from Joint Base Lewis-McChord (JBLM) to an undisclosed location 115 km south and 112 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?

Answer 1

5 minutes 4.8 seconds

Explanation:

We can work this problem several ways. One is to determine the component of the distance from JBLM to the mountain that is in the direction the plane is flying. We can do that by finding the dot product of the vector to the mountain with the normalized direction vector of the airplane:

JA = JR•(JP/|JP|) . . . . . . where JR = (56, -40) and JP = (112, -115)

= (56, -40)•(112, -115)/√(112² +115²)

JA = 10872/√25769 ≈ 67.7268 . . . . km

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At a speed of 800 km/h, this distance will be covered in ...

time = distance/speed

time = (67.7268 km)/(800 km/h) = 0.0846585 h

That's about 5 minutes, 4.8 seconds.

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In the attached diagram, J represents JBLM, R represents Mt. Rainier, A represents the point of closest approach, and P would represent the location of the airplane after 1 hour of flying time, (112, -115). In the above, we have used the names of these line segments/vectors.