# Homework Help: Hailstone latent heat problem

1. Dec 16, 2012

### DLH112

1. The problem statement, all variables and given/known data
Assume that a hailstone at 0◦C falls through
air at a uniform temperature of 0◦C and lands
on a sidewalk also at this temperature.
From what initial height must the hailstone fall in order to entirely melt on impact? The acceleration due to gravity is
9.8 m/sec2
and the latent heat of fusion of
water is 3.3 × 10^5 J/kg .

2. Relevant equations

3. The attempt at a solution
I'm guessing it has to do with calculating the time based on the acceleration and height. Or maybe something to do with work being done by gravity. In any case, it seems weird that it doesnt give the mass of the hailstone. We only briefly went over this stuff on the last day of class, and I couldnt find anything too similar in the book.

2. Dec 16, 2012

### rock.freak667

Yes the work being done by gravity is what will provide the latent energy for the ice to melt. So if you equate those two, what are you left with?

3. Dec 16, 2012

### DLH112

ah i see. something like mgh = mL and the mass cancels so gh = L or h = L/9.8

edit: 9.8 m/s2 h = 330000 J/kg
h = 330000/9.8
h = 3367.46939 m or 3.367469 km? this is wrong though... maybe i got some units wrong?

Last edited: Dec 16, 2012
4. Dec 16, 2012

### rock.freak667

That should be correct, why do you say it is wrong?

5. Dec 16, 2012

### DLH112

its an online homework thing. it said that answer is wrong

6. Dec 16, 2012

### Staff: Mentor

You lost a power of ten when you did the division.

7. Dec 16, 2012

### DLH112

oh wow, thanks, im blind xD