Aski lift is used to transport people from the base of a hill to the top. if the lift leaves thebase at a velocity of 15.5 m/s and arrives at the top with a final velocity of 0 m/s, what is the height of the hill? round the answer to the nearest tenth. 

The energy of the ski lift at the base is kinetic energy:

where m is the mass of the ski lift+the people carried, and  is velocity at the base.
As long as the ski lift goes upward, its velocity decreases and its kinetic energy converts into potential energy. Eventually, when it reaches the top, its final velocity is v=0, so no kinetic energy is left and it has all converted into gravitational potential energy, which is 

where  and h is the height at the top of the hill.

So, since the total energy must conserve, we have

and so

from which we find the height: