1980 AMC 12 Problem 9
Attempt Problem 9 of the 1980 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1980 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
9.
A man walks miles due west, turns to his left and walks miles in the new direction. If he finishes at a point miles from his starting point, then is
not uniquely determined by the given
information
Answer: E
Small hint:
Resolve the second walk into horizontal and vertical components
Big hint:
The distance equation is quadratic in ; check whether both positive roots are valid
Solution:
Take east as the positive horizontal direction. After the turn, the -mile displacement has components Therefore Hence giving or The value is not unique.
Therefore, the correct answer is E.
Problem 9 in other years
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