A plane is traveling at north east direction, 30° regard to the north. if not wind it could travel at 60 m/s but it results that there is wind going to the east at 20 m/s. determine the resulting speed of the plane regard to earth.

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Physics

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10 May, 05:00

A plane is traveling at north east direction, 30° regard to the north. if not wind it could travel at 60 m/s but it results that there is wind going to the east at 20 m/s. determine the resulting speed of the plane regard to earth.

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Johanna Romero · Answer 1

Speed of the plane regard to earth = 72.1110 m/s

Explanation:

First we decompose the plane's velocity on the horizontal and vertical X-axis, taking into account the deviation of the direction of the plane 30 ° with respect to the north to the east:

Vx = (60m/s) * sen (30°) = 30 m/s

Vy = (60m/s) * cos (30°) = 59.9615m/s

The wind speed only has component in the horizontal X axis since it has east direction:

Vx = 20 m/s

We add the components of the wind on the X axis and then the components on the Y axis to be able to determine the resulting velocity using the Pythagorean theorem, taking as the hypotenuse result and the X and Y components the catheters. This result will be the final speed of the plane with respect to Earth:

Vx = (20m/s) + (30m/s) = 50m/s

Vy = 59.9615m/s

V = √ ((50m/s) ² + (59.9615m/s) ²) = 72.1110m/s