Calculating the Initial Height of a Hailstone for Complete Melting on Impact

[DLH112]

Homework Statement

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 .
Answer in units of km

Homework Equations

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 doesn't give the mass of the hailstone. We only briefly went over this stuff on the last day of class, and I couldn't find anything too similar in the book.

 

[rock.freak667]

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 doesn't give the mass of the hailstone. We only briefly went over this stuff on the last day of class, and I couldn't find anything too similar in the book.

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?

 

[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?

 

[rock.freak667]

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

 

[DLH112]

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

 

[gneill]

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

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

 

[DLH112]

oh wow, thanks, I am blind xD