The magnituA (2.0i + 2.0j) mSolution You may wish to draw the vectors to conceptualize- (2.01 - 4.0) mandB =the situation. We calegorize this as a simple plug-in problem.Comparing this expression for A with the general expres-sion A A, i + A,j, we see that A= 2.0 m and A, = 2.0 m.We can fir= - 4.0 m. We obtain the resul-= 2.0 m and BLikewise, Btant vector R, using Equation 3.14:R = A + B = (2.0 + 2.0) i m + (2.0 – 4.0)f m(4.0i – 2.0j) mYour ctan%3Dmeanbeenor= 4.0 mR, = - 2.0 mthe +Example 3.4 The Resultant DisplacementYourA particle undergoes three consecutive displacements:the c(15i + 30j + 12k) cm, d = (23i – 14j - 5.0k) cn%3DO Cm,di%3Dand dg = (-- 13i + 15j) cm. Find the components of theresultant displacement and its magnitude.%3Dsionto thon Three-dinmensional displacements are more diffi-imagine than those in two dimensions, because thecan be drawn on paper. For this problem, let us concep-e that you start with your pencil at the origin of a pieceSTaph paper on which you have drawn x and y axes. Moveur pencil 15 cm to the right along the x axis, then 30 cmapward along the y axis, and then 12 cm vertically away fromthe graph paper. This provides the displacement describedby d1. From this point, move your pencil 23 cm to the rightparallel to the x axis, 14 cm parallel to the graph paper inthe -y direction, and then 5.0 cm vertically downward to-forthisnizeTHR.ward the graph paper. You are now at the displacementfrom the origin described by d + d2. From this point, moveyour pencil 13 cm to the left in the-x direction, and (fi-nally!) 15 cm parallel to the graph paper along the y axis.Example 3.5 Taking a Hike

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Description: The magnituA (2.0i + 2.0j) mSolution You may wish to draw the vectors to conceptualize- (2.01 - 4.0) mandB =the situation. We calegorize this as a simple plug-in problem.Comparing this expression for A with the general expres-sion A A, i + A,j, we s

We know that using triangle law we find out here resultant of these displacements and magnitude.…

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A particle undergoes three consecutive displacements: di and d3 = (-13i + 15j) cm. Find the components of the resultant displacement and its magnitude. (15i + 30j + 12k) cm, d = (23i – 14j – 5.0k) cm %3D %3D %3D

A particle undergoes three consecutive displacements: di and d3 = (-13i + 15j) cm. Find the components of the resultant displacement and its magnitude. (15i + 30j + 12k) cm, d = (23i – 14j – 5.0k) cm %3D %3D %3D

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Topic Video

Question

The magnitu
A (2.0i + 2.0j) m
Solution You may wish to draw the vectors to conceptualize
- (2.01 - 4.0) m
and
B =
the situation. We calegorize this as a simple plug-in problem.
Comparing this expression for A with the general expres-
sion A A, i + A,j, we see that A= 2.0 m and A, = 2.0 m.
We can fir
= - 4.0 m. We obtain the resul-
= 2.0 m and B
Likewise, B
tant vector R, using Equation 3.14:
R = A + B = (2.0 + 2.0) i m + (2.0 – 4.0)f m
(4.0i – 2.0j) m
Your c
tan
%3D
mean
been
or
= 4.0 m
R, = - 2.0 m
the +
Example 3.4 The Resultant Displacement
Your
A particle undergoes three consecutive displacements:
the c
(15i + 30j + 12k) cm, d = (23i – 14j - 5.0k) cn
%3D
O Cm,
di
%3D
and dg = (-- 13i + 15j) cm. Find the components of the
resultant displacement and its magnitude.
%3D
sion
to th
on Three-dinmensional displacements are more diffi-
imagine than those in two dimensions, because the
can be drawn on paper. For this problem, let us concep-
e that you start with your pencil at the origin of a piece
STaph paper on which you have drawn x and y axes. Move
ur pencil 15 cm to the right along the x axis, then 30 cm
apward along the y axis, and then 12 cm vertically away from
the graph paper. This provides the displacement described
by d1. From this point, move your pencil 23 cm to the right
parallel to the x axis, 14 cm parallel to the graph paper in
the -y direction, and then 5.0 cm vertically downward to-
for
this
nize
TH
R.
ward the graph paper. You are now at the displacement
from the origin described by d + d2. From this point, move
your pencil 13 cm to the left in the-x direction, and (fi-
nally!) 15 cm parallel to the graph paper along the y axis.
Example 3.5 Taking a Hike

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