An archer fires an arrow at an angle of 9° above the horizontal with a resultant velocity of 24 m/s

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

What kind of simple machine is a catapult?

3. a worker pushes a 30.5 kg polished stone along a polished table with a force on bonin a straight line for 5.20 s after starting from rest. there is no friction between thestone and the table. at the end of the table. the stone is hooked to a cable with a lengthof 62.0 cm to rotate it to a rough table to store until they can be picked up. the roughtable has a coefficient of static friction 0.702 with the polished stone. remember that 8= 9.80 m/s2a) what is the speed of the stone when it is hooked to the cable? b) what is the tension in the cable while the stone is rotating? (there is still nofriction)c) how much force is needed to make the stone begin sliding from rest on therough table? ius = 0.70262.0 cm30.5 kg20.5 kg6= 0