Question

What is the magnitude of the upward thrust force (assumed constant)?Express your answer with the appropriate units

Answer 1

Complete Question

A helicopter of mass  $1.40 *10^{3}$ kg is descending vertically at 3.00 m/s. The pilot increases the upward thrust provided by the main rotor so that the vertical speed decreases to 0.450 m/s as the helicopter descends 5.00 m. What is the magnitude of the upward thrust force (assumed constant)?Express your answer with the appropriate units.

Answer:

The value is  $F = 11257 \ N$

Explanation:

From the question we are told that

   The mass of the helicopter is  $m = 1.40 *10^{3} \ kg$

   The initial descending speed is $u= 3.00 \ m/s$

   The  descending speed after the upward thrust has been increased is $v = 0.450 \ m/s$

    The  height when descending speed is $v = 0.450 \ m/s$  is  $s = 5.0 \ m$

Generally according to the kinematics equations

   $v^2 = u^2 + 2(a)s$

Here a is the acceleration due to gravity plus the acceleration of the helicopter

So

    a  =  $a = -g + a_h$

the negative sign is due to the fact that the direction of the plane is in the negative y axis

So

       $v^2 = u^2 + 2(-g + a_h)s$

=>    $0.45^2  =  3^2  + 2(-9.9 + a_h) * 5$

=>   $a_h = \frac{-8.7975}{5} + 9.8$    

=>   $a_h = 8.0405 \ m/s^2$    

Generally the thrust force is mathematically represented as

     $F = m * a_h$

=> $F = 1.40 *10^{3} * 8.0405$

=> $F = 11257 \ N$