An airplane has an airspeed of 450 km/hr bearing N45E. The wind velocity is 30 km/hr in the direction N30W. What is the ground speed and what is its direction?.
I have gotten this far:
A= 450cos(45), 450sin(45) = (318.20, 318.20)
W= 30cos(120), 30sin(120) = (-15, 25.98)
A+W= 303.2 +344.18
|A+W|= 458.7 km.hr
tan-1(344.18/303.2)= 48.62
How do I change 48.62 to degrees east of north, which is the actual direction if the aircraft relative to due north (round to the nearest tenth degree).
Our answers are identical:
458.7km/hr @ 48.62 deg. CCW.
90 - 48.62 = 41.38 deg,E of N.
You did a good job on this problem!
Well, to change 48.62 to degrees east of north, you can just subtract it from 90 degrees. So, 90 - 48.62 = 41.4 degrees. Therefore, the direction of the airplane relative to due north is N41.4E. Don't you think that's a rather clever way of saying it's slightly to the right of straight ahead?
To change the direction from 48.62 degrees to degrees east of north, you need to subtract it from 90 degrees. This is because if you consider the north direction as 0 degrees, the east direction is 90 degrees.
So, subtracting 48.62 from 90, we get:
90 - 48.62 = 41.38 degrees
Therefore, the direction of the airplane relative to due north, rounded to the nearest tenth degree, is 41.4 degrees east of north.
To change the direction 48.62 degrees to degrees east of north, we can subtract it from 90 degrees.
90 degrees - 48.62 degrees = 41.38 degrees
So, the direction of the airplane relative to due north is 41.4 degrees east of north.