WTW218 student is standing on the slopes of a curiously smooth and symmetric mountain. Consulting his map, he notices that if he introduces a suitable coordinate system, then the height (in meters) of a point with coordinates (r, y) is h(x, y) = 2000 – 1000 (x2 + y²). He is standing at the point with coordinates (100, 200). (a) What is his present elevation? (b) How many meters is he below the top of the mountain? (c) In which direction from where he is standing does the ground slope upwards most steeply? (d) In which direction from where he is standing does the ground slope downwards most steeply? (e) In which directions from where he is standing can he walk without changing his elevation? (f) Determine all directions from where he is standing so that the ground changes with an elevation of 18 meters/second.
WTW218 student is standing on the slopes of a curiously smooth and symmetric mountain. Consulting his map, he notices that if he introduces a suitable coordinate system, then the height (in meters) of a point with coordinates (r, y) is h(x, y) = 2000 – 1000 (x2 + y²). He is standing at the point with coordinates (100, 200). (a) What is his present elevation? (b) How many meters is he below the top of the mountain? (c) In which direction from where he is standing does the ground slope upwards most steeply? (d) In which direction from where he is standing does the ground slope downwards most steeply? (e) In which directions from where he is standing can he walk without changing his elevation? (f) Determine all directions from where he is standing so that the ground changes with an elevation of 18 meters/second.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve from 2(d) to 2(f)
Transcribed Image Text:2. A WTW218 student is standing on the slopes of a curiously smooth and symmetric mountain.
Consulting his map, he notices that if he introduces a suitable coordinate system, then the height
(in meters) of a point with coordinates (x, y) is h(x, y) = 2000 – T000 (x² + y²). He is standing
at the point with coordinates (100, 200).
(a) What is his present elevation?
(b) How many meters is he below the top of the mountain?
(c) In which direction from where he is standing does the ground slope upwards most steeply?
(d) In which direction from where he is standing does the ground slope downwards most steeply?
(e) In which directions from where he is standing can he walk without changing his elevation?
(f) Determine all directions from where he is standing so that the ground changes with an
elevation of 18 meters/second.
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