Майор Вихрь
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Liz, you did everything right; I just didn't fully explain the conditions (because I didn't expect anyone to solve it). The specific heat capacity of ice is also given, and it's explained that for evaporation, you should simply calculate the heating up to 100 degrees. I was too lazy to do the calculations myself; I just derived the final formula. If I remember correctly, the answer was 2.3 km/s.
So, lambda in your formula is unnecessary (the ice particles are only heated; there's no need to calculate melting). Also, I think you forgot to multiply the kinetic energy by two (there are two ice particles).
O God of Earth and Altar,
Bow down and hear our cry,
Our earthly rulers falter,
Our people drift and die,
The walls of gold entomb us,
The swords of scorn divide,
Take not thy thunder from us,
Take away our pride.
G.K. Chesterton: English Hymnal
Bow down and hear our cry,
Our earthly rulers falter,
Our people drift and die,
The walls of gold entomb us,
The swords of scorn divide,
Take not thy thunder from us,
Take away our pride.
G.K. Chesterton: English Hymnal