The pilot of an airplane is trying to fly due west toward an airport. The airspeed...

The pilot of an airplane is trying to fly due west toward an airport. The airspeed of this plane is 900 km/hr. If the wind is blowing from the southwest at 100 km/hr, in what direction must his heading be? Find the speed of the plane relative to the ground.

Solutions

Expert Solution

v_wind = 100 km/hr (-cos45 i - sin45 j)

= - 70.7 i - 70.7 j km/h

v = v_wind + v_plane

v = (- 70.7i - 70.7j) + (900 cos(theta)i + 900 sin(theta)j)

v = (900 cos(theta) - 70.7)i + (900 sin(theta) - 70.7)j

v is along west.

so component along j will be zero.

900 sin(theta) - 70.7 = 0

sin(theta) = 4.5 deg North to west .....Ans

Speed of plane relative to ground

v = - 900 cos4.5 - 70.7

v = 968 km/ h ...........Ans

genius_generous answered 1 year ago

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