Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem P. 4467. (October 2012)

P. 4467. A police car parking on the hard shoulder of a highway, is passed by a car at a speed of 108 km/h. (This is the greatest speed at which this car can travel.) After a short time it turns out in the police car that the passing car is a stolen one. The police car starts to chase the car ten seconds after the stolen car passed it. The maximum speed of the four-wheel drived police car is 162 km/h. The coefficient of static friction between the road and the wheels is 0.4. In order not to reach the traffic in the city it would be good to catch the escaping car in a distance of 1.5 km. Is it possible?

(4 pont)

Deadline expired on November 12, 2012.


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

Megoldásvázlat. Ha a rendőrautó egyenletesen gyorsulna a csúcssebesség eléréséig, akkor utolérné a menekülőt. Mivel a légellenállás a sebesség növekedtével egyre jobban fékezi az autót, a csúcssebességet csak csökkenő gyorsulással közelíti meg; emiatt éppen nem éri utol a lopott kocsit 1500 méteren belül. (Megfelelő indoklás és számolás esetén mindkét változatot elfogadjuk.)


Statistics:

221 students sent a solution.
4 points:141 students.
3 points:39 students.
2 points:16 students.
1 point:22 students.
0 point:3 students.

Problems in Physics of KöMaL, October 2012