A stone of mass 500 g is thrown vertically upwards with a velocity of 15ms^-1.

Calculate:

(a) the potential energy at the greatest height,

(b) the kinetic energy on reaching the ground

(c) the total energy at its half waypoint.

A metal ball of mass 2kg is allowed to fall freely from rest from a height of 5m above the ground.

1. Taking g = 10ms^-1, calculate:
   
   1. the potential energy possessed by the ball when it is initially at rest.
   2. the kinetic energy of the ball just before it hits the ground?
2. What happens to the mechanical energy after the ball hits the ground and comes to rest?

The diagram given below shows a ski jump. A skier weighing 60kgf stands at A at the top of ski jump. He moves from A and takes off for his jump at B.

(a) Calculate the change in the gravitational potential energy of the skier between A and B.

(b) If 75% of the energy in part (a) becomes the kinetic energy at B, calculate the speed at which the skier arrives at B.

(Take g = 10 ms^-2).

(c) Does total mechanical energy change during the ski jump?

A hydroelectric power station takes its water from a lake whose water level is 50m above the turbine. Assuming an overall efficiency of 40%, calculate the mass of water which must flow through the turbine each second to produce power output of 1MW. (Take g = 10 m s^-2).