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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:
[tex]E=P+K[/tex]
2) At the beginning of the motion, the total energy of the object is just potential energy:
[tex]E_1=P=mgh[/tex]
where m is the mass, [tex]g=9.81~m/s^2[/tex] is the gravitational acceleration, and [tex]h=4.2~m[/tex] 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
[tex]E_2= \frac{1}{2}mv^2 [/tex]
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
[tex]E_1 = E_2[/tex]
and so:
[tex]mgh= \frac{1}{2}mv^2 [/tex]
from which we can find v, the velocity:
[tex]v= \sqrt{2gh}= \sqrt{2\cdot9.81~m/s^2 \cdot 4.2~m}=9.08~m/s [/tex]
