Question

A hiker starts at his camp and moves the following distances while exploring his surroundings: 74.0 m north, 2.20 ? 10² m east, 1.20 ? 10² m at an angle 30.0

Answer 1

draw out the vectors on graph paper

take north as y
and take east as plus x

first vector is (0, 75)
second is (250, 0)
forth is (0, -150)

the third had an angle that is harder
use sine and cosine to figure out the x and y

30 deg north of east means you go east then turn 30 degs up so its 30 degs from x

if its 125 m total thats the hypotenuese

cos A = x/h
x = h cos A

sin A = y/h
y = h sin A

since A = 30
x = 125 * sqrt (3)/2

y = 125 * sin 30 = 125 * 0.5

the third vector is ( 62.5*sqrt(3) , 62.5)

so now we have all vectors just add them up x with x and y with y whats left tells you the displacement if you find the distance to of the hypoteneuse

first vector is (0, 75)
second is (250, 0)
forth is (0, -150)

these add to (250, -75)

the third vector is ( 62.5*sqrt(3) , 62.5)
then add the last one

the displacement vector is ( 250 + 62.5*sqrt3 , -12.5)

displacement = sqrt((250 + 62.5*sqrt3)^2 + (12.5)^2)

displacement = 358.5 m

b) no the order does not matter