8. monica took a train 30 miles south to cincinnati. then she took a different train 18 miles east. draw a vector diagram showing monica's trip, including the resultant vector. be sure to label all vectors. (5 points)

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

Waves that cause the most damage during an earthquake are a. surface waves c. s waves b. p waves d. ocean waves

Which of the following changes will result in a stronger electromagnet? a. using fewer coils of wire b. using a higher voltage c. using a shorter nail d. using a longer wire