Is the first question worked right and any hints on the second please

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SUMMARY

The discussion focuses on calculating the mass of a helicopter based on the downward velocity of air displaced by its rotor blades. The initial calculation yielded a force of 9409N and a mass of 940kg, which was confirmed as correct. In the second part, the upward acceleration of the helicopter was calculated incorrectly; the correct approach requires accounting for the difference in forces due to the change in air velocity from 12 m/s to 13 m/s. The final upward acceleration was determined to be 1.7 m/s².

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electricsound
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1. The rotating blade of a hovering helicopter sweeps out an area of radius 4m imparting a downward velocity of 12ms^-1 to the air displaced. Find the mass of the helicopter.
(g=10ms^-2, density of air= 1.3 kgm^-3)

The Attempt at a Solution


F=d/dt(mv)
F= (density of air*volume)*12
= 1.3*pie*16*12*12
=9409N
mass of helicopter= 940kg (the answers matched, but is it worked correct?)

2. The speed of rotation of the blades of the helicopter in question 1 is increased so that the air now hasa downward velocity of 13ms^-1. Find the upward acceleration of the helicopter.
attempt at the solution
F=mv
11043N=1.3(pie*16*13*13
F=ma
11043N=940*a

11043/940=a

Actual answer= 1.7ms^-2
 
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The first part looks right, but in the second part remember that the 12 m/s air velocity just held the helicopter stationary. So to calculate the acceleration, you need to calculate the difference between the force that held the helicopter stationary (12 m/s air) and the increased air velocity (13 m/s air.). You calculated the entire force from the 13 m/s air and forgot to subtract off that part of the force which is compensating gravity.
 

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