Answer :
The acceleration of the Cessna 172 airplane is [tex]\(2.21 \text{ m/s}^2\)[/tex].
To find the acceleration of the Cessna 172 airplane, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. This can be expressed with the formula:
[tex]\[ F = m \cdot a \][/tex]
where [tex]\(F\)[/tex] is the force, [tex]\(m\)[/tex] is the mass, and [tex]\(a\)[/tex] is the acceleration.
Given that the net force [tex]\(F\)[/tex] acting on the airplane is 1900 N and the mass [tex]\(m\)[/tex] of the airplane is 860 kg, we can rearrange the formula to solve for acceleration [tex]\(a\)[/tex]:
[tex]\[ a = \frac{F}{m} \][/tex]
Substituting the given values:
[tex]\[ a = \frac{1900 \text{ N}}{860 \text{ kg}} \][/tex]
[tex]\[ a = 2.209255813953488 \text{ m/s}^2 \][/tex]
Rounding to two decimal places, the acceleration of the airplane is approximately:
[tex]\[ a \approx 2.21 \text{ m/s}^2 \][/tex]
Therefore, the acceleration of the Cessna 172 airplane is [tex]\(2.21 \text{ m/s}^2\)[/tex] in the positive x direction.
Final answer:
The Cessna 172 airplane, with a net force of 1900 N and a mass of 860 kg, is accelerating at approximately 2.21 m/s^2 in the positive x direction.
Explanation:
The acceleration of the airplane can be found by using the formula from Newton's second law of motion: Force = mass * acceleration. In this case, the force is 1900 N, and the mass of the Cessna 172 airplane is 860 kg. The acceleration, therefore, can be calculated by rearranging the formula: Acceleration = Force/mass.
Therefore, the acceleration of the airplane is 1900 N / 860 kg, which equals approximately 2.21 m/s^2 in the positive x direction.
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