Question

An airplane flies 120 km at a constant altitude in a direction 30.0° north of east. a wind is blowing that results in a net horizontal force on the plane due to the air of 2.40 kn in a direction 10.0° south of west. how much work is done on the plane by the air?

Answer 1

 Best Answer:  The net angle between the direction of flight of the aircraft and the wind in the opposing direction is 20. THe component opposing the aircraft is 2.4*cos 20 KN 
= 2400 * 0.9397 = 2255.2622 N. The distance covered is 120 Km 
The work done by the aircraft overcoming the wind is 
= 2255.2622 * 120000 = 270631464 = 2.71 x 10^8 N 
As the question is trickily worded as : the work done on the plane by the air (wind) the answer is -2.71 x 10^8 J . (fourth option)

Answer 2

-2.71 × 10⁸ J of work is done on the plane by the air

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Further explanation

Let's recall the formula of Work and Kinetic Energy as follows:

$\boxed {E_k = \frac{1}{2}mv^2 }$

$\boxed {W = Fd }$

Ek = Kinetic Energy ( Newton )

m = Object's Mass ( kg )

v = Speed of Object ( m/s )

W = Work ( Joule )

F = magnitude of Force ( N )

d = displacement ( m )

Let us now tackle the problem !

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Given:

displacement of airplane = d = 120 km = 1.2 × 10⁵ m

direction of velocity of airplane = θ = 30.0° North of East

horizontal force of the wind = f = 2.40 kN = 2.40 × 10³ N

direction of the force = α = 10.0° South of West

Asked:

work done on the plane by the air = W = ?

Solution:

We will use Work formula to solve this problem as follows:

$W = F d$

$W = - f d \cos \beta$

$W = - f d \cos (\theta - \alpha)$

$W = - (2.40 \times 10^3) \times (1.2 \times 10^5) \times \cos ( 30.0^o - 10.0^o )$

$W \approx - 2.71 \times 10^8 \texttt{ J}$

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Negative sign means the direction of force is opposite to the direction of displacement.

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Learn more

• Impacts of Gravity : https://brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454
• The Acceleration Due To Gravity : https://brainly.com/question/4189441
• Newton's Law of Motion: https://brainly.com/question/10431582
• Example of Newton's Law: https://brainly.com/question/498822

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics