How do I figure out this vector problem?

Question

On a safari, a team of naturalists sets out toward a research station located 5.2 km away in a direction 42 degrees north of east. After traveling in a straight line for 2.5 km, they stop and discover that they have been traveling 29 degrees north of east, because their guide misread his compass. What are the magnitude and direction (relative to due east) of the displacement vector now required to bring the team to the research station?
magnitude ________ km
direction ________ degrees (north of due east)

Answer 1

plot the path in an x-y diagram. East is +x and north is +y.
use cm instead of km.

Last plot the vector back to the origen and solve the triangles by trigonometry.

Answer 2

They want to get to a point 5.2 km at 42° from the origin. In rectangular coordinates, this is:
(5.2 cos 42°, 5.2 sin 42°)
= (5.2 · 0.7431448, 5.2 · 0.6691306)
= (3.864353, 3.479479)

After 2.5 km at 29°, they're at:
(2.5 cos 29°, 2.5 sin 29°)
= (2.5 · 0.8746197, 2.5 · 0.4848096)
= (2.186549, 1.212024)

The distance between these points is the magnitude.
d = √[(x1 - x0)² + (y1 - y0)²]
= √[(3.864353 - 2.186549)² + (3.479479 - 1.212024)²]
= √[(1.677804)² + (2.267455)²]
= √[2.815026262416 + 5.141352177025]
= √7.956378439441
= 2.82 km

The ratio of Δy to Δx is the tangent of the angle of direction.
a = atan [(y1 - y0) / (x1 - x0)]
= atan [(3.479479 - 1.212024) / (3.864353 - 2.186549)]
= atan [2.267455 / 1.677804]
= atan [1.351442]
= 53.5°

Answer 3

I used the same method and got the exact same result as Louise. There may be an easier way to do it but I don't know what it is offhand.

Answer 4

Obviously if you dont know how to do vectors since you ahve multiple posts, you should pay attention in class, attend class, or get help!

noone on here wants to do your homework for you!