(a) 7861 N
Along the vertical direction, the plane is moving at constant velocity: this means that the net vertical acceleration is zero, so the vertical component of the 8420 N upward force is balanced by the weight (pointing downward).
The vertical component of the upward force is given by:
[tex]F_y = F sin \theta[/tex]
where
F = 8420 N is the magnitude of the force
[tex]\theta=69.0^{\circ}[/tex] is the angle above the horizontal
Substituting,
[tex]F_y = (8420 N)(sin 69.0^{\circ}) =7861 N[/tex]
This means that the weight of the plane is also 7861 N.
(b) 3.87 m/s^2
From the weight of the plane, we can calculate its mass:
[tex]m=\frac{W}{g}=\frac{7861 N}{9.8 m/s^2}=802 kg[/tex]
Where g = 9.8 m/s^2 is the acceleration due to gravity.
Along the horizontal direction, the 8420 N is not balanced by any other backward force: so, there is a net acceleration along this direction.
The horizontal component of the force is given by
[tex]F_x = F cos \theta = (8420 N)(cos 69.0^{\circ})=3107 N[/tex]
According to Newton's second law, the net force along the horizontal direction is equal to the product between the plane's mass and the horizontal acceleration:
[tex]F_x = m a_x[/tex]
so if we solve for a_x, we find:
[tex]a_x = \frac{F_x}{m}=\frac{3107 N}{802 kg}=3.87 m/s^2[/tex]
