Atennis ball is thrown vertically upward with an initial velocity of +6.2 m/s. what will the ball’s velocity be when it returns to its starting point? the acceleration of gravity is 9.81 m/s 2 . answer in units of m/s.

Find the vertex(use the completing the square method), findthe x- and y-intercepts, and sketch the graph offunction. y = 2x2 + 4x - 1

The most important difference between a wedge and an inclined plane is a. their size b. their shape c. how they are used d. what they are made of

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