Answer:
Part a)

Part b)

Explanation:
Resistance of the solenoid is given as
R = 4.10 ohm
now we have

here we know that



now from above formula


Part a)
now we know that it is wounded over the solenoid
so here we can say



Part b)
now length of solenoid is given as



Answer:
160790 J
Explanation:
We can find the heat necessary for the ice to go from -20 degrees Celsius to 0 degrees Celsius:

Where
is the specific heat of ice, that is the amount of heat that must be supplied per unit mass to raise its temperature in a unit.

We must calculate the latent heat of fusion required for this ice mass to change to water:

Where H=334 J/g is the specific latent heat of fusion of water, that is the amount of energy needed per unit mass of a substance at its melting point to change from the solid to the liquid state.

Then we calculate the heat necessary for the water to go from 0 degrees Celsius to 20 degrees Celsius:

Where
is the specific heat of water, that is the amount of heat that must be supplied per unit mass to raise its temperature in a unit.

Finally the 3 results are added:

25,000 Feet = 7620m
PE = mgh where m is mass, g is gravity accel: 9.8 n h is height
= 90 x 9.8 x 7620
= 6720840J
= 6.72MJ
F = ma where m is mass, a is accel = gravity = 9.8
= 90 x 9.8
= 882N
Accel = gravity = 9.8m/s^2
KE = 1/2mv^2 where m is mass n v is vel
if no wind resistance, PE leaving airplane = KE at net
6720840 = 1/2 x 90 x v^2
v^2 = 149352
v = 386.5m/s
150MPH=67m/s
@150MPH, his speed is not changing so accel=0
accel=0, force=0 by newton's second law
force=0 when wind resistance = gravity = 9.8m/s^2
by conservation of energy, Luke's KE = PE = mgh = 6720840J
he was unhurt cuz' his momentum was absorbed by the net