Aaron finds a pirate’s treasure map. the treasure map says to start at an oak tree and walks 111 feet east and 234 feet south from the tree. how far did the pirate walk? what is the displacement vector for the pirate? what is the distance and direction relative to east?

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

If we relied solely on the nonrenewable resources found in the u. s., which one would we run out of first at current usage levels? a. natural gas b. oil c. uranium d. coal

Why is the use of carbon-14 limited