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use the ke and gpe equations to solve for speed or height depending on the situation.

a 1,000-kg car has 50,000 joules of kinetic energy. what is its speed?
( show work)

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 law represents the thermodynamic statement of the conservation of energy of a system? a. the fourth law b. the first law c. the second law d. the third law

Need people build a dam to create a reservoir that supplies water a nearby city needs. describe two ways this action will likely affect the water cycle in the local environment. (5 points) worth 20 points