A delivery truck travels 18 blocks north, 10 blocks east, and 16 blocks south.?

Question

What is the final displacement from the origin (magnitude and direction)? Assume the blocks are equal length.

a) 10 blocks, 11 degrees north of east

b) 14 blocks, 16 degrees north of east

c) 12 blocks, east

d) 15 blocks, north

Please explain how to do this. I am so lost...

Answer 1

Truck travels | Line Coordinates

------------------+-------------------...

18 North........| 0, 0; 0, 18

10 East.........| 0, 18; 10, 18,

16 South.......| 10, 18; 10, 2

-----------------+----------------

This forms a right triangle where:

a = 10

b = 2

c = √(10² +2² )

c = 10.12 - round to 10

arctan (2/10) = 11.31° ENE - round to 11° ENE

a.) Is the closet answer

Answer 2

Mathes - geometry- draw the picture and then use Pythagoras' theorem for the displacement = sqrt (easting^2 + northing^2)

Answer 3

va=9.816 i + 1.9081 j

vb=13.458 i + 3.859 j

vc=12i+0j=

vd=0i+15j

x= 35.274

y= 20.7671

final displacement from the origin:

V=sqr(35.274^2+(20.7671)^2) = 40.933 blocks

direction:

atan(20.7671/35.274)*180/3.14159

= 30.487 degrees north of east

need more detail, let me know.