Question

A commercial jet is flying from Miami to Seattle. The jet’s velocity with respect to the air is 580 miles per hour, and its bearing angle is 332 degrees. The wind, at the altitude of the jet, is blowing from the southwest with a velocity of 60 miles per hour. Write the velocity of the jet relative to the air as a vector in component form.

Answer 1

the velocity of the jet relative to the air as a vector in component form = (-272.3î + 525.7j) miles per hour

Explanation:

The velocity of the jet with respect to the air is described to have a magnitude of 580 miles per hour with a bearing of 332°.

Converting the bearing to the angle the velocity vector makes with the positive x-axis in the anti-clockwise direction, we have

θ = 360° - 332° + 90 = 118°

The bearing and the angle converted is shown in the attached image.

Velocity vector of the jet's speed relative to air is given as

Magnitude [(cos θ)î + (sin θ)j] = (580cos 118°)î + (580sin 118°)j = (-272.3î + 525.7j) miles per hour