Triangle PQR with area A is given in a plane parallel to the gravitational acceleration g, with the length QR perpendicular to g, and the point P is above QR.

Now we let two blocks (considered as points) slide down PQ and PR respectively. This gives the different times t1 and t2 respectively for each block. If one of the angles Q or R is obtuse, the corresponding block will slide on the inside of the triangle.

If we assume there is no friction, find the minimum of T=t1+t2 in terms of A and g and determine the triangle when this occurs.

   PQR is an equilateral triangle and

     T^4 = (32/(3*g))^2*A*sqrt(3)

Posted by Bractals on 2008-07-01 18:50:29