Pluto has a mass of 1.27x1022 kg and a radius of 1.14x109 m. (a) An astronaut throws a rock at 12 m/s at an angle of 25° above horizontal from a height of 3.25 m above
the surface. How far horizontally does the rock travel before hitting the surface of Pluto?

Using the given data table, calculate the acceleration of the skateboarder. you can use either form of the equation below?

How does the image distance (di) of a convex lens compare with the image distance of a concave lens? a. the image distance of the convex lens is positive, and that of the concave lens is negative. b. both are negative for a virtual image. c. both are positive for a virtual image d. the image distance of the convex lens is negative, and that of the concave lens is positive.

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