Mathematical and Physical Journal
for High Schools
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# Problem P. 4046. (February 2008)

P. 4046. The figure shows a smooth vertical path. On the left-handside there is a ramp, the incline angle is =45o, than it is continued with a semi-circle of radius R, and then there is a parabola at the end. The symmetry axis of the parabola is vertical, and the parabola is open above. If a body travel through the path without friction, the normal force exerted on it does not change abruptly at the border of the semicircle and the parabola.

a) What is the height h of the parabola?

b) What is the least height H, measured from the ground, at which an object should be released in order to go through the whole path?

(5 pont)

Deadline expired on March 11, 2008.

### Statistics:

 53 students sent a solution. 5 points: Almási 270 Gábor András, Berta Katalin, Blázsik Zoltán, Csató Bertalan, Deák Zsolt, Dein Zsolt, Földes Tamás, Gaál Alexisz Tamás, Gál Bálint, Hartstein Máté, Hegyi Ádám, Hlatky Dávid, Iván Dávid, Kovács 235 Gábor, Kovács 888 Gábor, Krämer Zsolt, Kupcsik Réka, Lászlóffy András, Maknics András, Marák Károly, Nagy 648 Donát, Pásztor Ádám Viktor, Patartics Bálint, Pázmán Koppány, Rárósi Dávid, Szabó 666 Dániel, Szolnoki Lénárd, Tolnai Gábor, Veres 001 Máté, Vőfély Róza Villő. 4 points: Balassa Péter, Boros Csanád Örs, Csengeri Béla, Deli Gábor, Fialowski Melinda, Fonyó Dávid, Jakab Dávid, Lovas Lia Izabella, Ölvedi Tibor, Para Attila, Zsolczai Viktor. 2 points: 6 students. 1 point: 4 students. 0 point: 2 students.

Problems in Physics of KöMaL, February 2008