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