an airplane, flying in the direction of 35 degree east of north at 325 mph in still air, encounter a 40-mph tail wind acting in the direction 50 degree west of north. the airplane maintains its compass heading but, because of the wind, acquires a new ground speed and direction. what are they?
whats the new ground speed?
whats is the new direction angle (thats east of north)?
This question calls for vector addition.
Pretend the sky is on an x-y plane. If the airplane is go east of north at 35°. It is in quadrant I.
Therefore, the i and j component are positive
Airplane = 325mph[sin35°i + cos35°j]
The wind is acting in quadrant II which means it is going in the positive y, negative x.
Wind = 40mph[-sin50°i + cos50°j]
The new vector for the plane is airplane + wind = [325mph*sin35°i - 40mph*sin50°i + 325mph*cos35°j + 40mph*cos50°j] = [155.77mph i + 291.94mph j]
New direction is arctan(155.77/291.94) = 28.08°from the y axis
And a new ground speed of (155.77^2 + 291.94^2)^(1/2) = 330.90mph
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