Answer:
a) The potential energy in the system is greatest at X.
Explanation:
Let be X the point where a ball rests at the top of a hill. By applying the Principle of Energy Conservation, the total energy in the physical system remains constant and gravitational potential energy at the top of the hill is equal to the sum of kinetic energy, a lower gravitational energy and dissipated work due to nonconservative forces (friction, dragging).

Conclusions are showed as follows:
a) The potential energy in the system is greatest at X.
b) The kinetic energy is the lowest at X and Z.
c) Total energy remains constant as the ball moves from X to Y.
Hence, the correct answer is A.
I am not as sure but I think it is 9.469 miles
Answer:
work output is always less than work input - the ratio is less than 1.
Explanation:
This principle comes from the fact that a machine or system cannot produce more work than is supplied to it, because this would violate the energy conservation law (work is a type of mechanical energy).
In theoretical machines called "ideal machines" the input work is the same as the output work, but these machines are only theoretical because in real applications there is always some type of energy loss, either in heat produced by a machine or processes for its operation, for this reason the output work is always less than the input work.
Regarding the ratio work output to work input:

because work input WI is always greater than work output WO.
Answer:
True! First step is to make objective observations.
Answer:
v=32.9m/s
Explanation:
The acceleration needed to mantain a circular motion of radius r and speed v is given by the equation 
This is the centripetal acceleration. The person will feel what is called a centrifugal acceleration, of the same value, because he is not in an inertial frame (thus subject to fictitious forces, product of inertia).
We want to know the speed of his head when it is subject to 12.5 times the value of the acceleration of gravity while moving on a 8.84m radius circle, so we must do:
