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C. 981. The captain of a ship wrote down the formula d=p\sqrt h in his log book for the distance to the horizon. Unfortunately, the number p got blurred. d denotes the distance to the horizon in kilometers, and h stands for the height of the eyes of the observer above sea level in metres. Determine a value of p that provides a practicable formula. (Use 6370 km for the radius of the Earth.)

(5 points)

Deadline expired.


Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás. Készítsünk ábrát.

Pitagorasz-tétellel: \left(\frac{h}{1000}+R\right)^2=R^2+d^2, amiből d=\sqrt h\cdot\sqrt{\frac{h}{10^6}+\frac{2R}{10^3}}. Ha h kicsi és R=6370 km, akkor p=\sqrt{\frac{h}{10^6}+\frac{2R}{10^3}}\approx 3,57 km.


Statistics on problem C. 981.
171 students sent a solution.
5 points:79 students.
4 points:18 students.
3 points:55 students.
2 points:11 students.
1 point:1 student.
0 point:2 students.
Unfair, not evaluated:5 solutions.


  • Problems in Mathematics of KöMaL, March 2009

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