Answer to Question #121671 in Quantum Mechanics for Vusimuzi Mohlamme

Question #121671
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?
Note on the meaning of 1E8 in answers: 1E8 is an alternative way to write "10 to the power of 8". So 1E8 is 100 000 000. It is a convenient notation when superscripts are difficult to accommodate.
1
Expert's answer
2020-06-11T10:34:37-0400

Let, the distance traveled by airplane d=120km=12×104md=120km=12\times 10^4m and force acting on it by air is F=2.40kN=2.4×103NF=2.40kN=2.4\times10^3N ,

Now, draw the free body diagram


As, we know that , work done by a force is

W=Fd=Fdcos(θ)W=\overrightarrow{F}\cdot\overrightarrow{d}=Fd\cos(\theta)

Where, θ\theta angle between F\overrightarrow{F} and d\overrightarrow{d} .

Here,

θ=60+10=70\theta=60^{\circ}+10^{\circ}=70^{\circ}

Thus,

W=2.4×103×12×104cos(70)    W=9.85×107JW=2.4\times10^3\times12\times10^4\cos(70^{\circ})\\ \implies W=9.85\times10^7J


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