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In: Physics

A 21500 kg jet airplane is flying through some high winds. At some point in time,...

A 21500 kg jet airplane is flying through some high winds. At some point in time, the airplane is pointing due north, while the wind is blowing from the north and east. If the force on the plane from the jet engines is 35500 N due north, and the force from the wind is 14700 N in a direction 75.0° south of west, what will be the magnitude and direction of the plane's acceleration at that moment? Enter the direction of the acceleration as an angle measured from due west (positive for clockwise, negative for counterclockwise).

Expert Solution

Let the positive y-direction points from south to north and the positive x-direction point from east to west. The force of the engine is along the y-axis.

The wind force makes 75^o with the x-axis. The wind force is

Note that x-component is positive because the force vector lean in the postive x-direction, and y-component is negative because wind force lean in the negative y-direction.

The net force is the vector sum of the engine force and the wind force

Using newton's second law of motion, the acceleration of the plane is

The magnitude of the acceleration is

The angle that the net force makes with the west direction is

genius_generous answered 2 months ago

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