A playground is on the flat roof of a city school, 6.2m above the street below. The vertical wall of the building is h=7.30m high, forming a 1.1-m-high railing around the playground. A ball has fallen to the street below, and a passerby returns it by launching it at an angle of
θ
=53.0 degrees above the horizontal at a point d=24.0m from the base of the building wall. The ball takes 2.20s to reach a point vertically above the wall.

a) Find the speed at which the ball was launched. (Give your answer to two decimal places to reduce rounding errors in later parts.)
b) Find the vertical distance by which the ball clears the wall.
c) Find the horizontal distance from the wall to the point on the roof where the ball lands.

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

Which object is most likely represented by a dot?

Which statement correctly describes a step-up transformer? a. it increases the amount of electric energy available. b. it increases the voltage of an electric current. c. it changes direct current into alternating current. d. it has more loops of wire in its primary coil.