Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem C. 981. (March 2009)

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 pont)

Deadline expired on April 15, 2009.


Sorry, the solution is available only in Hungarian. Google translation

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:

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