(Optics disguised as mechanics) In the bottom half of the cartesian plane (y < 0) the potential energy is UB and in the top half it is UT (both are constants). A particle with y < 0 is headed toward the the top half-plane with an initial kinetic energy TB at angle ϕB relative to the y axis. At what speed and angle ϕT does it emerge into the upper half of the plane? Discuss the relationship to Ibn Sahl's (aka Snell's) law that you remember from your elementary E&M class (PHYS119 if at UNC).

the only real purpose of sputnik 1 was to beat the us into space. we were getting close to launching a useful satellite, explorer 1 - which launched on january 31, 1958. the ussr had to beat that, so they launched sputnik 1 on october 4, 19

no. bullets are macro objects. wave nature is for light waves, extremely tiny particles. if a light particle was the size of your finger, the bullet would be the size of the universe. so basically, that huge difference in size makes the wave nature of matter insignificant.