Please show work it\'s saying 30.2 mins doesn\'t work so I know it\'s not that.
ID: 1468195 • Letter: P
Question
Please show work it's saying 30.2 mins doesn't work so I know it's not that. I've tried it.When the wind is blowing an average of 42.8 mph, a wind tower with its propellors centered at a height of 40 m off the ground is supplied with energy at a rate of 14.0 kW. A large bank of batteries collects the energy from the wind tower. If the efficiency of each object (tower, cable, battery) is 82.0%, how long will it take for the bank of batteries to collect 20.8 MJ of energy. (Express your answer in minutes.) Number min
Explanation / Answer
wind velocity is V = 42.8 mph = 0.011 m/s
height h = 40 m
P = 14 kW
given energy is 20.8 MJ = 20.8 X 106 J = KE
KE = 1 / 2 m V2 then
1 / 2 m V2 = 20.8 X 106
0.5 X m X 0.0112 = 20.8 X 106
m X 6.05 X 10-5 = 20.8 X 106
m = 3.43 X 1011 kg
power rate we have P = m g h / t
rearranging for time t = m g h / P
t = 3.43 X 1011 X 9.8 X 40 / 14 X 103
t = 1344.56 X 1011 / 14 X 103
t = 96.04 X 108 sec
t = 1.600 X 108 min
this is the for the total energy
but given is about only 0.82 %
so
t = 0.82 X 1.600 X 108
t = 1.31 X 108 min