I agree, it is wrong. Secondly, the units are wrong, I just don't understand your units.
http://www.jiskha.com/display.cgi?id=1272226772
I got 31560 kg*m/s but its wrong.
http://www.jiskha.com/display.cgi?id=1272226772
The momentum of the air flowing downward must be equal in magnitude and opposite in direction to the momentum of the helicopter upward, to maintain a hovering position.
The formula for momentum is given by:
p = m * v
Where:
p is the momentum
m is the mass
v is the velocity
In this case, the velocity of the air flowing downward is given as 59.0 m/s.
Let's assume that the mass of air passing through the helicopter blades every second is 'm'.
According to the conservation of momentum, the momentum of the air downward is equal to the momentum of the helicopter upward. Therefore:
m * (-59.0 m/s) = (5350 kg) * (0 m/s)
Since the helicopter is hovering, its velocity is zero, so the momentum of the helicopter upward is zero.
Simplifying the equation, we can solve for 'm':
m = (0 kg * m/s) / (-59.0 m/s)
m = 0 kg
This means that no mass of air is required to pass through the blades every second for the helicopter to hover.
It's important to note that this result is idealized and assumes perfect hovering without any loss or wastage of airflow. In practice, there will always be some air movement, but the actual mass required for hovering will depend on additional factors such as the design and efficiency of the helicopter.