Hail Storm

Your plan worked beautifully! The minions woke up this morning with lots of boils. They're miserable and packing up to go home. There is also a rumor going around that this plague of boils is a punishment by God because they are hurting animals—they don't suspect A.A.K.V.O. at all!

Unfortunately, there was one other camp of six V.A.L.A. agents separate from the main camp and they've been collecting Slow Lorises all day! You must save them but you don't want them to know that A.A.K.V.O. is responsible. Since they are already worried about plagues from God, you decide to give them another one: a Plague of Hail Stones!

You plan to drop golf-ball sized hail (2 cm radius) on the remaining V.A.L.A. agents from a helicopter 4 km up. Hail is very rare in the tropics so they will likely think it is another sign from God. It is hot in Java (30 °C) so you are worried about the ice balls melting before they can fall to the ground.What percentage will melt while they fall? How much bigger should you make them so they are golf-ball sized by the time they reach the ground?

Hints:

• You can get the velocity at which hail stones fall from this website.
• From that you can get the time they will take to fall in seconds
• The amount of heat lost (H) in Joules/second is H = C * A * (T2 - T1) where C is the coefficient of heat transfer (estimate from this website at 35 J/s*m²*°C), A is the surface area of the hail stone in m², T2 is the temperature of the air in °C, and T1 is the temperature of the ice in °C (in this case, the freezing temperature of water)
• Once you have the amount of heat lost in Joules/sec, you can calculate the total amount of heat lost in Joules during the fall
• It takes 333 Joules to melt 1 g of ice. You can now figure out how many grams of ice will melt during the fall
• From the radius of the hail stone, you can calculate the volume in cm³. Ice weighs 0.934 g per cm³ so you can calculate how much each hail stone weighs.
• Now you know how much each hail stone weighs and how much ice it loses during the fall. What percentage of ice is lost during the fall?