Question

A hiker starts at his camp and moves the following distances while exploring his surroundings: 70.0 m north, 2.60 x 10^2m east, 110 m at an angle 30.0° north of east, and 1.50 x 10^2m south.
(a) Find his resultant displacement from camp. (Take east as the positive x-direction and north as the positive y-direction.)

magnitude ____ m
direction ____ ° south of east

(b) Would changes in the order in which the hiker makes the given displacements alter his final position? Explain.

Answer 1

It's not clear from the problem as written what "2.60" and "1.50" are. Can shed some light on that?

Answer 2

Sorry! It's corrected, thanks for letting me know!

Answer 3

So if each of those moves is a vector, we need to assign a coordinate system and signs to the vectors. So let's say that north is positive y, and south is negative y. East is positive x, and west is negative x.

Answer 4

Hopefully you know that vectors can have components. In this case of our coordinate system, a vector can have an x component and a y component. Note however that any vector that is parallel to the x-axis will only have an x-component. Likewise, any vector parallel to the y-axis will have only y component.

Answer 5

When we add vectors, we add like components. So if one vector is u=<v,w> and another is r=<s,t>, u+r=<(v+s),(w+t)>.

Answer 6

Three of your given vectors are parallel to the axes of the coordinate system. One isn't, and for that one you need to find its components.

Answer 7

The x component of a vector is given by:\[v _{x}=||v||\cos \left( \theta \right)\]and the y component is given by:\[v _{y}=||v||\sin \left( \theta \right)\]This means that the vector v can be written as:\[v=<v _{x},v _{y}>\]

Answer 8

Are beginning to see how to do the problem?