One way to reduce the cost of lifting mass into orbit is to use a linear accelerator to drive a payload up to escape velocity (or thereabouts) and then let it go. This way one doesn't have to lift the fuel used to lift the fuel used to lift the ...(almost all the fuel used in a rocket is used to lift fuel, not payload).
Assume that fusion energy has been developed and electricity is cheap, and that high temperature superconductors have made such a mass driver feasible. Your job is to do a first estimate of the design parameters.
A proposed plan for the mass driver is shown above. The track is 100
kilometers long and slopes gently upwards. The payload capsule has a
mass of 
kg (two metric tons). The head of the track
is high in the Andes, 
kilometers from the center of the
earth.
a) Neglecting air resistance, find the escape velocity for the capsule. Although bound orbits will not require quite as much energy, air resistance will dissipate some energy. Either way, this is a reasonable estimate of the velocity the driver must be able to produce.
b) Assuming that the capsule is started from rest and that a constant
tangential force accelerates it, find the tangential force necessary
to achieve escape velocity at the end of the track. Note: Ignore the
normal force that the track must exert to divert it so that it departs
at an upward angle.) From this find the acceleration of the capsule,
in multiples of 
. Is this acceleration likely to be tolerable to
humans?