A CESSNA Citation attains an airspeed of 640 km/hr. The plane sets out for a destination...
A CESSNA Citation attains an airspeed of 640 km/hr. The plane sets out for a destination 1120 km to the north (a 0° course) but discovers that the plane must be headed 20° east of north to fly there directly. The plane arrives in 2.00 h.
a) What is the wind speed?
b) What is the direction of the wind? Give your answer in ° where North = 0°, East = 90°, South = 180°, and West = 270°.
Homework Answers
Vgs =1120 km/(2 h) j =(560 km/h) j
Vas =(640 km/h)*cos 70 i +(640 km/h)*sin 70 j
=218.89 i + 601.40 j km/h
The ground velocity of the plane is equal to the air velocity plus the velocity of the wind.
Vgs =Vas +Vw
Vw =Vgs -Vas
=(-218.89 i - 41.4 j )km/h
wind speed Vw =sqrt(218.89^2+41.4^2) =222.77 km/h =223 km/h
b)
theta =arctan(-41.4/-218.89) =10.7 degrees south of west
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