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kondor19780726 [428]

3 years ago

10

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 hori

zontal 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?

2 answers:

astraxan [27]3 years ago

6 0

Best Answer:<span> </span><span>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)</span>

emmainna [20.7K]3 years ago

6 0

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

$\texttt{ }$

<h3>Further explanation</h3>

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

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

$\boxed {W = Fd }$

<em>Ek = Kinetic Energy ( Newton )</em>

<em>m = Object's Mass ( kg )</em>

<em>v = Speed of Object ( m/s )</em>

<em>W = Work ( Joule )</em>

<em>F = magnitude of Force ( N )</em>

<em>d = displacement ( m )</em>

Let us now tackle the problem !

$\texttt{ }$

<u>Given:</u>

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

<u>Asked:</u>

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

<u>Solution:</u>

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

$W = F d$

$W = - f d \cos \beta$

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

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

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

$\texttt{ }$

<em>Negative sign</em> means the direction of force is opposite to the direction of displacement.

$\texttt{ }$

<h3>Learn more</h3>

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

$\texttt{ }$

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Dynamics

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