The lowest point in Death Valley is 85 m below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 m. A) What is the change in potential energy of an energetic 63.2 kgkg hiker who makes it from the floor of Death Valley to the top of Mt.Whitney? B) If a frictionless track was constructed from the top of Mt. Whitney to the bottom of Death Valley such that a roller coaster car was allowed to run on the track without air resistance, how fast would the car be moving when it reached the bottom?

A basketball player throws a basketball m = 1 kg straight up with an initial speed of v0 = 9.5 m/s. The ball leaves his hand at shoulder height h0 = 2.2 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g.

Geometric Optics & Images Problem 6:   Fiber optics are an important part of our modern internet. In these fibers, two different glasses are used to confine the light by total internal reflection at the critical angle for the interface between the core (ncore = 1.505 ) and the cladding (ncladding = 1.451). Part (a)  Numerically, what is the largest angle (in degrees) a ray will make with respect to the interface of the fiber θmax, and still experience total internal reflection?  Part (b)  Suppose you wanted the largest angle at which total internal reflection occurred to be θmax = 5 degrees. What index of refraction does the cladding need to be if the core is unchanged?

A 31 kg bear slides, from rest, 10 m down a lodgepole pine tree, moving with a speed of 3.0 m/s just before hitting the ground. (a) What change occurs in the gravitational potential energy of the bear-Earth system during the slide? (b) What is the kinetic energy of the bear just before hitting the ground? (c) What is the average frictional force that acts on the sliding bear?