500 mph east relative to the ground. A Cessna is flying at 150 mph 60° north of west relative to the ground. What is the Cessna's speed relative to the 747? A 634 mph B 578 mph C 590 mph D 444 mph E 610 mph

Answer :

Answer:

option C

Explanation:

given,

Flight speed in east = 500 mph

Cessna flying = 150 mph

At an angle = 60°  N of W

angle, θ = 180° - 60° = 120° N of W

Relative velocity  between them

[tex]\vec{V_{ab}} = \vec{v_{b}} - \vec{v_{a}}[/tex]

[tex]\vec{V_a} = 500 \hat{i}[/tex]

[tex]\vec{V_b} = 150(cos 120^0 \hat{i}+ sin 120^0 \hat{j})[/tex]

[tex]\vec{V_b} = -75 \hat{i} +129.9 \hat{j}[/tex]

now,

[tex]\vec{V_{ab}} = -75 \hat{i} +129.9 \hat{j} -500 \hat{i}[/tex]

[tex]\vec{V_{ab}} = -575 \hat{i} + 129.9 \hat{j}[/tex]

magnitude of the relative velocity

[tex]v = \sqrt{(-575)^2 + 129.9^2}[/tex]

   v = 589.5 mph

Relative speed of the Cessna's = 590 mph.

Hence, the correct answer is option C

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