Magyar Information Contest Journal Articles

# Problem P. 4817. (February 2016)

P. 4817. The owner of a dog throws a ball into the river perpendicularly to the riverbank. The ball hits the water 5 metres away. The speed of the current is 0.3 m/s and the dog can swim at a speed of 0.5 m/s with respect to the water.

$\displaystyle a)$ Where and when will the dog reach the ball if it leaps into the water at the moment when the ball hit the water, and it swims towards the ball all the time?

$\displaystyle b)$ After reaching the ball the dog immediately starts to swim towards its owner. The motion of the dog is uniform straight line motion, such that the direction of the velocity of the dog with respect to the riverbank points towards the owner all the time. How much time elapses from the moment the dog reached the ball until it gives it back to its owner?

$\displaystyle c)$ The owner throws the ball again into the water in the same way as he did previously. The dog reaches the ball again, but when it brings it back it swims along a curved path such that its velocity with respect to the water points towards its owner. After reaching the ball how much time elapses until the dog gives the ball back to its owner? (Hint: Compare the rate of change of the distance between the owner and the dog to that component of the dog's velocity, which is parallel to the current.)

In which case is the time during which the dog brings back the ball shorter, and what is the time difference between these two cases?

(6 pont)

Deadline expired on 10 March 2016.

### Statistics:

 32 students sent a solution. 6 points: Asztalos Bogdán, Balogh Menyhért, Bekes Nándor, Blum Balázs, Büki Máté, Csenger Géza, Fajszi Bulcsú, Fehér 169 Szilveszter, Fekete Balázs Attila, Forrai Botond, Iván Balázs, Kasza Bence, Kovács Péter Tamás, Nagy 555 Botond, Németh 777 Róbert, Olosz Adél, Páhoki Tamás, Sal Kristóf, Szentivánszki Soma , Szick Dániel, Tomcsányi Gergely, Varga-Umbrich Eszter. 5 points: Molnár Mátyás. 4 points: 4 students. 3 points: 1 student. 2 points: 3 students. 1 point: 1 student.

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