The law of conservation of energy states that the total energy of a system remains constant if no external work is done on the system. Therefore, the total mechanical energy of the car/rider combination at the top of the hill must be equal to the total mechanical energy of the car/rider combination at the bottom of the hill.
At the top of the hill, the total mechanical energy of the car/rider combination is:
E_top = mgh
where m is the mass of the car/rider combination, g is the acceleration due to gravity, and h is the height of the hill.
At the bottom of the hill, the total mechanical energy of the car/rider combination is:
E_bottom = 1/2mv^2
where m is the mass of the car/rider combination and v is the velocity of the car/rider combination at the bottom of the hill.
We can set these two expressions equal to each other:
mgh = 1/2mv^2
Simplifying and solving for v, we get:
v = sqrt(2gh)
where sqrt represents the square root function.
Substituting the given values, we have:
v = sqrt(2*9.8*65162.5)
v = 359.2 m/s
Therefore, the kinetic energy of the car/rider combination at the bottom of the hill is:
E_kinetic = 1/2mv^2
E_kinetic = 1/2*80*(359.2)^2
E_kinetic = 5,200,179.2 J
Rounding to the nearest tenth, the kinetic energy of the car/rider combination at the bottom of the hill is approximately 5,200,179.2 J.