New one; (because we are SMP damn it)
Imagine two points A and C that are at the same horizontal level (C slightly lower than A actually by a tiny bit that wont matter here initially) and a distance d horizontally from each other. Now imagine point B lower than A,C and between them forming a triangle ABC.
Find the coordinates of B as functions of coordinates of A,C (basically only the distance between them AC) that makes the time it takes for an object to slide from A to C minimum under the influence of vertical direction gravity g without friction. At B the object has a smooth transition using a very quick curvy part that we can ignore its size compared to the distance between A-C).
Now imagine C is a bit lower than A indeed (say by h) and there is friction coefficient μ. Investigate as function of μ if it is possible to go from A to C and what location for B (ie what triangle ABC) makes the time minimum as functions of h, μ, d.
Lets create problems to challenge this page;
https://www.physics.harvard.edu/acad...rgrad/problems
And have fun with great problems from there here in more organized presentation format;
http://www.people.fas.harvard.edu/~djmorin/Chapter1.pdf (over the years SMP has seen several from this list like the dragon problem, the two envelopes etc)
Last edited by masque de Z; 12-24-2018 at 07:47 PM.