Vectors word problem?
A plane heads due east and travels 300 km. Then, the plane turns 25° south of east and travels another 75 km. Next, the plane turns due north and travels 500 km. Then, the plane heads due west and travels 55 km. Finally, the plane turns 35° south of west and travels 400 km? How for away (km) from the original point is the plane? (The resultant)
Favorite Answer
= 300 + 75cos25 – 55 – 400cos35
= -14.688km
Total distance travelled south
= 75sin25 – 500 + 400sin 35
= -238.873km
The plane’s final distance from the starting point is:
sqrt(14.688^2 + 238.873^2)
= 239.324km.
If the final direction from the starting point is N x deg W, then:
tan(x) = 14.688 / 238.873
x = 3.52.
The plane ends up 239.324km N 3.52deg W of the starting point.
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