Answer :
The keep the 830-kg helicopter aloft, approximately 203.35 kg/s of air must be pushed downward at 40.0 m/s.
To keep the helicopter aloft, the downward force due to gravity must be balanced by an equal and opposite upward force generated by pushing air downward. We can calculate the amount of air that needs to be pushed downward using the concept of momentum conservation.
The downward force due to gravity on the helicopter is given by:
Force gravity = mass * acceleration due to gravity
Force gravity = 830 kg * 9.8 m/s²
Force gravity = 8134 N
To balance this force, the upward force generated by pushing air downward must be 8134 N.
Now, let's calculate the amount of air that needs to be pushed downward at 40.0 m/s:
Force upward = mass air * velocity air
To find the mass of air, we rearrange the equation:
mass air = Force upward / velocity air
mass air = 8134 N / 40.0 m/s
mass air = 203.35 kg
Therefore, to keep the 830-kg helicopter aloft, approximately 203.35 kg/s of air must be pushed downward at 40.0 m/s.
The correct answer is: 203 kg/s.
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