In the qualifying round of the 50-yd freestyle in the sectional swimming championship, Dugan got an early lead by finishing the first 25.00 yd in 10.01 seconds. Dugan finished the return leg (25.00 yd distance) in 10.22 seconds. Determine Dugan's average velocity for the entire race. Number only, round to the nearest hundredth.

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

Unpolarized light whose intensity is 1.19 w/ is incident on a polarizer. (a) what is the intensity of the light leaving the polarizer? (b) if the analyzer is set at an angle of = 41.0∘ with respect to the polarizer, what is the intensity of the light that reaches the photocell?

Avector of magnitude 2 cannot be added to a vector of magnitude 3 so that the magnitude of the resultant is a. zero b. 1 c. 3 d. 5 e. 7