Question

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.

Answer 1

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

Step-by-step 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