(10) What is the final velocity of the box if it is given a push at the top of the hill just great enough to overcome static friction?
The final velocity of the box can be found using the energy of the system. The energy at the bottom of the hill is entirely kinetic. The magnitude of the kinetic energy is equal to the potential energy at the top of the hill minus the energy lost to friction. This calculation can be used to find the final velocity:
