A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 4.0º to the hor
izontal. If friction forces are ignored, how far along the hill does she travel before stopping?
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The amount of heat given by the water to the block of ice can be calculated by using
where
is the mass of the water
is the specific heat capacity of water
is the variation of temperature of the water.
Using these numbers, we find
This is the amount of heat released by the water, but this is exactly equal to the amount of heat absorbed by the ice, used to melt it into water according to the formula:
where
is the mass of the ice while 
is the specific latent heat of fusion of the ice.
Re-arranging this formula and using the heat Q that we found previously, we can calculate the mass of the ice:
where
Using these numbers, we find
This is the amount of heat released by the water, but this is exactly equal to the amount of heat absorbed by the ice, used to melt it into water according to the formula:
where
Re-arranging this formula and using the heat Q that we found previously, we can calculate the mass of the ice: