Tutorial Exercise A person going for a walk follows the path shown in the figure, where y₁ = 319 m and = 65.0°. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? End 200 m Step 3 End, Q Start 100 m 200 m Step 1 The dark arrow on the figure represents the resultant displacement from the starting point to the end of the path. This vector is at an angle p from the negative x axis as drawn in the figure. From the figure, it looks as if the person walked at least three times as far as the magnitude of the resulting displacement. 30.0 Start 100 m 9 R 30 3/₁ 150 m Y₁ 150 m x îm jm Step 2 We are given that the total trip consists of four straight-line paths whose lengths are as follows: d₁ = 100 m, d₂ = 319 m, d3= 150 m, and d4 = 200 m. The resultant displacement R is equal to the sum of the four individual displacements, so we have the resultant displacement R=d₁ + d₂ + d3 + ď4. X We translate from the pictorial representation to a mathematical representation by writing the individual displacements in unit-vector notation, paying close attention to the angles in the figure and signs on the components. First, write the two displacement vectors in unit-vector notation that are along the positive x and negative y directions, respectively.
Tutorial Exercise A person going for a walk follows the path shown in the figure, where y₁ = 319 m and = 65.0°. The total trip consists of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the starting point? End 200 m Step 3 End, Q Start 100 m 200 m Step 1 The dark arrow on the figure represents the resultant displacement from the starting point to the end of the path. This vector is at an angle p from the negative x axis as drawn in the figure. From the figure, it looks as if the person walked at least three times as far as the magnitude of the resulting displacement. 30.0 Start 100 m 9 R 30 3/₁ 150 m Y₁ 150 m x îm jm Step 2 We are given that the total trip consists of four straight-line paths whose lengths are as follows: d₁ = 100 m, d₂ = 319 m, d3= 150 m, and d4 = 200 m. The resultant displacement R is equal to the sum of the four individual displacements, so we have the resultant displacement R=d₁ + d₂ + d3 + ď4. X We translate from the pictorial representation to a mathematical representation by writing the individual displacements in unit-vector notation, paying close attention to the angles in the figure and signs on the components. First, write the two displacement vectors in unit-vector notation that are along the positive x and negative y directions, respectively.
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter3: Vectors
Section: Chapter Questions
Problem 35AP: A person going for a walk follows the path shown in Figure P3.35. The total trip consists of four...
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Transcribed Image Text:Tutorial Exercise
A person going for a walk follows the path shown in the figure, where y₁ = 319 m and 8 = 65.0°. The total trip consists
of four straight-line paths. At the end of the walk, what is the person's resultant displacement measured from the
starting point?
End
200 m
End,
-
d₂
Ꮎ
Start 100 m
Step 1
The dark arrow on the figure represents the resultant displacement from the starting point to the end of the path. This
vector is at an angle from the negative x axis as drawn in the figure. From the figure, it looks as if the person walked
at least three times as far as the magnitude of the resulting displacement.
y₁
Start 100 m
200 m
Ꮎ .
=
R
30.0°
30°
150 m
3₁₁
150 m
Y₁
Step 2
We are given that the total trip consists of four straight-line paths whose lengths are as follows: d₁ = 100 m,
d₂ = 319 m, d3= 150 m, and d4 = 200 m. The resultant displacement R is equal to the sum of the four individual
displacements, so we have the resultant displacement R = ₁ + d₂ + ď₂ + ď4.
d3
->
Step 3
We translate from the pictorial representation to a mathematical representation by writing the individual displacements
in unit-vector notation, paying close attention to the angles in the figure and signs on the components.
x
First, write the two displacement vectors in unit-vector notation that are along the positive x and negative y directions,
respectively.
îm
jm
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