Explain why it is not possible to add a scalar to a vector.
If you take two steps of different sizes, can you end up at your starting point? More generally, can two vectors with different magnitudes ever add to zero? Can three or more?
Problems&Exercises
Use graphical methods to solve these problems. You may assume data taken from graphs is accurate to three digits.
Find the following for path A in
[link] : (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.
(a)
(b)
,
east of north
Find the following for path B in
[link] : (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.
Find the north and east components of the displacement for the hikers shown in
[link] .
north component 3.21 km, east component 3.83 km
Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements
and
, as in
[link] , then this problem asks you to find their sum
.)
Suppose you first walk 12.0 m in a direction
west of north and then 20.0 m in a direction
south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements
and
, as in
[link] , then this problem finds their sum
.)
,
south of west
Repeat the problem above, but reverse the order of the two legs of the walk; show that you get the same final result. That is, you first walk leg
, which is 20.0 m in a direction exactly
south of west, and then leg
, which is 12.0 m in a direction exactly
west of north. (This problem shows that
.)
(a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction
north of east (which is equivalent to subtracting
from
—that is, to finding
). (b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction
south of west and then 12.0 m in a direction
east of south (which is equivalent to subtracting
from
—that is, to finding
). Show that this is the case.
(a)
,
north of east
(b)
,
south of west
Show that the
order of addition of three vectors does not affect their sum. Show this property by choosing any three vectors
,
, and
, all having different lengths and directions. Find the sum
then find their sum when added in a different order and show the result is the same. (There are five other orders in which
,
, and
can be added; choose only one.)
Show that the sum of the vectors discussed in
[link] gives the result shown in
[link] .
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Receive real-time job alerts and never miss the right job again
Source:
OpenStax, Sample chapters: openstax college physics for ap® courses. OpenStax CNX. Oct 23, 2015 Download for free at http://legacy.cnx.org/content/col11896/1.9
Google Play and the Google Play logo are trademarks of Google Inc.
Notification Switch
Would you like to follow the 'Sample chapters: openstax college physics for ap® courses' conversation and receive update notifications?