Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem P. 4478. (November 2012)

P. 4478. A cyclist is riding his bicycle all out while he goes uphill at a speed of v1=12 km/h, and he can go downhill, on the same slope, at a speed of v2=36 km/h. What is his top speed on the level road, if his maximum strength to ride the bike is independent of the speed of the bicycle?

(5 pont)

Deadline expired on December 10, 2012.

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

Megoldásvázlat. Feltételezve, hogy a kerékpárt fékező erő egy sebességfüggetlen csapágysúrlódási erő és egy - a sebesség négyzetével arányos - közegellenállási erő összege,

$\displaystyle v_{\rm max}=\sqrt{\frac{v_1^2+v_2^2}{2}}\approx 27~\rm km/h.$

### Statistics:

 136 students sent a solution. 5 points: 85 students. 3 points: 11 students. 2 points: 3 students. 1 point: 8 students. 0 point: 25 students. Unfair, not evaluated: 4 solutions.

Problems in Physics of KöMaL, November 2012