PLease help on this question. Through explanation is appreciated

Question

A 3000kg helicopter, tilted as shown, is flying horizontally (neither gaining nor losing altitude). The helicopter is experiencing a 1200N drag.

How many forces are acting on the helicopter?

Are all the forces on the helicopter balanced?

What is the magnitude of the thrust?

What is the magnitude of the net force on the helicopter?

What is the magnitude of the helicopter's acceleration?

Describe the helicopter's speed. (increasing/decreasing/constant)

______________

\ |

14 degrees \ helicopter(tilt)|

_______________\___________|

Answer 1

Let

m = 3000 kg be the mass of the helicopter,

α be the degree of tilt against the vertical,

D = 1200 N be drag,

g = 9.81 m/s² be gravitational acceleration.

Your picture does not make it clear whether the 14° angle is against the vertical or horizontal.

Therefore I will show a solution for some angle α against the vertical.

You need to pug in α = 14° or α = 76° depending on the actual helicopter's orientation.

There are three forces acting on the helicopter:

the drag D, the unknown thrust T, and gravity mg.

The net force is their vector sum.

We are told that the helicopter is not gaining or loosing altitude.

That implies that the vertical component of the net force must be 0.

Let's see who contributes to that vertical component of the net force.

The drag D has no vertical component.

The thrust has vertical component Tcos(α) directed up.

Gravity has vertical component mg directed down.

Therefore

Tcos(α) = mg

So

T = mg/cos(α)

Now compute the horizontal component of the net force, which is the only one that could be non-zero.

Gravity contributes nothing to the horizontal component.

Thrust has horizontal component Tsin(α) oriented forwards.

Drag D is oriented backward.

So the net force F is

F = Tsin(α) - D = mgtan(α) - D

Whichever meaning you pick for the specification if tilt, the next force turns out positive,

which means that it is directed forward.

The helicopter's acceleration, a, by Newton's Second Law is

a = F/m = gtan(α) - D/m