If you know Trig (law of cosines, law of sines), very easy. make a sketch. You know two sides, and the included angle. Use law of cosines to find the third side of the triangle, then use law of sines to find the third angle (and use geometry of the vectors to figure true heading).
Now, if you dont know trig.
break both vectors into N, E components.
250:
250cos330 N + 250sin330 E
adding that to the second leg, we get the resultant to be:
250cos330 N + (250sin330+420)E
then, the angle is... Theta= arc tan Ecomponent/N component
and the magnitude is 250cos330/cosTheta
An aircraft travels 250 km on a heading of 330 degrees. It then turns due east and travels 420 km. How far and on what heading did it end up from it's starting point?
Please help!!!
2 answers
Displacement = 250km[330o] + 420km[0o].
Disp. = 250*Cos330+250*sin330 + 420,
Disp. = 216.5 - 234.9i + 420.
Disp. = 636.5 - 234.9ii = 678.5km[-20.3],
Disp. = 678.5km[20.3o] S. of E.
Disp. = 250*Cos330+250*sin330 + 420,
Disp. = 216.5 - 234.9i + 420.
Disp. = 636.5 - 234.9ii = 678.5km[-20.3],
Disp. = 678.5km[20.3o] S. of E.
1 answer