Problems for the 2014 University Physics Competition

Problem A:  Circumbinary Planets

Consider two stars, one with 50% of the mass of our Sun and one equal in mass to our Sun.  This binary star system has an orbital period of 30 Earth days.  Where could a planet have a stable orbit in this system?  Describe the possible stable planetary orbits.

Problem B:  A Water Fountain

A water fountain located at the middle of a circular pond ejects water straight up, and the water spreads out into a cone shape with the axis of the cone being vertical. As the water moves, its molecules collide with each other. Determine the probability that any molecule of the ejected water hits the pond at the point (x, y). Assume that the fountain’s ejection point is at (0, 0). From your model, determine the most probable place where the water lands and also the median circle, that is, that circle around the fountain inside which exactly half of the water lands. 

Papers must be submitted within 48 hours to solutions@uphysicsc.com