Answer to Question #85203 in Mechanics | Relativity for Maria

Question

An airplane whose air speed is 613 km/h is supposed to fly in a straight path 30.0 ∘ north of east. But a steady 86 km/h wind is blowing from the north.
In what direction should the plane head?

Answer 1

Vector velocity of a plane V_p = 613cos30⁰i + 613sin30⁰j

Vector velocity of the wind V_w = -86j

The direction in which the plane should go is the direction of the velocity of the plane relative to the wind

V_pw = V_p - V_w

V_pw =530.87i + 306.5j - (-86j) = 530.87i + 392.5j

Direction is given by tanθ = j/i = 392.5/530.87 = 0.739

Θ = arctan (0.739) = 36.48⁰ North of East

Answer: 36.48⁰ North of East