In the action adventure film Indiana Jones and the Raiders of the Lost Ark, Indiana Jones searches for the Ark of the Covenant. In one well-known nail biting scene Indiana tries to escape being crushed by a huge boulder rolling down a sloping terrain inside a tunnel. The rolling boulder of mass m rolls down the only path that Indiana Jones can take. Assume that the friction force between the sphere and the surface of the hill is negligible. At a particular time t1 the spherical boulder is at location 1 and moving with velocity v1. At a later time t2 the sphere is at location 2 and moving with velocity v2. Locations 1 and 2 are at vertical heights h1 and h2 respectively, from the bottom of the tunnel. When answering the following questions use 1 and 2 for subscripts to identify the different variables at the two different locations.

Part (a): U1 = mgh1
Part (b): What is the equation for translational kenetic energy, KT,1 of the spherical boulder?

KT,1 = .5mv12
Part (c): What is the equation for the rotational kinetic energy KR,1of the spherical boulder?
KR,1 = .5w12 ; KR,1 = (1/5)mv12

Part (d): What is the equation for the total kinetic energy Ktotal,1of the spherical boulder in terms of its linear speed?
Ktotal,1 = (7/10)mv12

Required:
Write the mathematical equation for the conservation of mechanical energy in terms of the mass, velocity, height and g.