Problem C. 981.

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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.

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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