At the top of a hill that is 4.37 meters high, a 70 kg skate boarder has 3000 1 point joules of potential energy. What is his speed at the bottom of the hill where
his potential energy is zero?

9.26m/s

Explanation:

Given parameters:

Height of the hill  = 4.37m

Mass of skate boarder = 70kg

Potential energy  = 3000J

Unknown:

Speed at the bottom of the hill  = ?

Solution:

At the bottom of the hill, the total potential energy is the same as the kinetic energy.

          Potential energy  = Kinetic energy

                  mgh  =  mv²  

                       2mgh  = mv²

                           v² = 2gh

                           v = √2gh

 g is the acceleration due to gravity

h is the height

                     v  = √2 x 9.8 x 4.37  = 9.26m/s

If the electrical energy put out by the turbine is the useful part
of the output, then the efficiency of the turbine is ...

     (the amount of electrical energy that's put out in some period of time)
divided by
     (the amount of energy put in during the same period of time,
      in the form of steam, falling water, kinetic energy of wind, etc.)