A hockey puck sliding on smooth ice at 4 m/s comes to a 1-m-high hill. Will it make it to the top of the hill?

No  it will not make to the top of the hill  

Explanation:

From the question we are told that

   The velocity is  

    The height of the hill is  

Generally from the law of energy conservation we have that

   The kinetic energy of the pluck at the level position =  The potential energy of the pluck at the maximum height the  pluck can get  to  

So

=>    

=>    

=>    

Given that the maximum height which the pluck can get to at this speed given in the question is less than the height of the hill then conclusion will be that the pluck will not make it to the top of the hill

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