Awagon is rolling forward on level ground. friction is negligible. the person sitting in the wagon is holding a rock. the total mass of the wagon, rider, and rock is 95.5 kg. the mass of the rock is 0.290 kg. initially the wagon is rolling forward at a speed of 0.510 m/s. then the person throws the rock with a speed of 17.5 m/s. both speeds are relative to the ground. find the speed of the wagon after the rock is thrown directly forward.

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

10 newton object is placed 3 meters from the fulcrum. at what distance on the other side would you need to place a 15 newton object to balance the lever? show your work!

What do you think car designers do if the damage caused by a crash test is too severe?