On an airplane's takeoff, the combined action of the air around the engines and wings of an airplane exerts a 8420-n force on the plane, directed upward at an angle of 69.0° above the horizontal. the plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. (a) what is the weight of the plane? n (b) what is its horizontal acceleration?

(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:

where

F = 8420 N is the magnitude of the force

is the angle above the horizontal

Substituting,

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:

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

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:

so if we solve for a_x, we find: