A block of ice falls and a part melts

[Karol]

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Homework Statement

A block of ice falls into a lake who's temperature is 0⁰c.
Half of a percent of it's mass melts. What is the minimum height the block falls from.

Homework Equations

The Latent heat of water:L=79.7[Cal/gr]
Potential energy: E_P=mgh

The Attempt at a Solution

the potential energy of the block transforms into heat which melts the ice.
I'm using L, the latent heat in [Cal/Kg] in order to be in the SI unit system and get the height h in meters:
mgh=79,700$\cdot$0.005$\cdot$m
$\Rightarrow$h=40[m]
The answer should be 171[m], according to the book.

 

[kuruman]

I'm using L, the latent heat in [Cal/Kg] in order to be in the SI unit system and get the height h in meters:
mgh=79,700$\cdot$0.005$\cdot$m
$\Rightarrow$h=40[m]
The answer should be 171[m], according to the book.

The SI unit for latent heat is Joules/kg not cal/kg.