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Answer:
5 minutes 4.8 seconds
Step-by-step 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.
