The compass of an airplane indicates that it is headed due n

The compass of an airplane indicates that it is headed due north, and its air speed indicator shows that it\'s moving throught the air at 180 km/h. If there is a wind of 75 km/h blowing from west to east, what is the velocity of the plane relative to the Earth.

Solution

we need to find the net velocity wrt to earth

we have wind blowing perpendicular to the velocity of plane.

so,

v wrt earth= sqrt ((180) ² + (75)²)

= 195 km /h

angle will be , arc tan ( 180/75) = 67.38 degrees north of east