A10.3 kg block of ice slides without friction down a long track. the start of the track is 4.2 m higher than the end of the track, and the path traveled is 8.0 m. find the speed of the block when it reaches the end of the track

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1) Since there is no friction between the ice and the track, there is no loss of energy in the motion, so we can apply the law of conservation of energy.
The total energy E (sum of potential energy P and kinetic energy K) must be conserved:
  

2) At the beginning of the motion, the total energy of the object is just potential energy:
 
where m is the mass,  is the gravitational acceleration, and  is the initial height of the body.

3) At the end of the motion, this potential energy has converted into kinetic energy, and so the total energy at this point is 

where m is the mass and v is the final velocity of the object.

4) We said that the total energy must be conserved, therefore we can write

and so:

from which we can find v, the velocity: