When the wind is blowing an average of 31.8 mph, a wind tower with its propellors centered at a height of 80 m off the ground is supplied with energy at a rate of 14.4 kW. A large bank of batteries collects the energy from the wind tower. If the efficiency of each object (tower, cable, battery) is 82.6%, how long will it take for the bank of batteries to collect 19.5 MJ of energy. (Express your answer in minutes.)

To solve this problem, we need to find the time it takes for the bank of batteries to collect 19.5 MJ (megajoules) of energy.

First, let's convert the wind power supplied to the tower to energy in megajoules.

Since power is given in kilowatts (kW) and energy is given in joules, we need to convert kilowatts to kilojoules by multiplying by 1,000. Then, we can convert kilojoules to megajoules by dividing by 1,000,000.

Given:
Wind power supplied = 14.4 kW
Time = ?
Energy collected = 19.5 MJ

Step 1: Convert wind power supplied to energy in megajoules.
14.4 kW * (1,000 J/1 kW) * (1 MJ/1,000,000 J) = 0.0144 MJ

Step 2: Calculate the efficiency of the system.
Efficiency = 82.6% = 0.826 (as a decimal)

Step 3: Calculate the effective energy collected by the bank of batteries.
Effective energy collected = Efficiency * Energy collected
Effective energy collected = 0.826 * 19.5 MJ = 16.067 MJ

Step 4: Calculate the time it takes to collect the effective energy.
Time = Effective energy collected / Energy collected per unit of time
Time = 16.067 MJ / 0.0144 MJ = 1,116.032 seconds

Step 5: Convert seconds to minutes.
1,116.032 seconds / 60 seconds/minute = 18.6 minutes

Therefore, it will take approximately 18.6 minutes for the bank of batteries to collect 19.5 MJ of energy.