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Point Particle Mechanics Question Bank
\[1\star\star\]
Ahmed's height
\[(4foot ,20 in ) \]
What is Ahmed's height in meters
\[h=1.72 m \;\;\;\;\;\;-C\]
\[ h=1.54 m \;\;\;\;\;\;-A\]
\[h=1.81 m \;\;\;\;\;\;-D\]
\[ h=1.62 m\;\;\;\;\;\;-B\]
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Choose the correct answer
\[2\star\]
Car speed
\[65 mil/h\]
Then the car speed in units of
\[m/s\]
equals
\[ 𝑣=82\;\; m/s \;\;\;\;\;\;-C\]
\[ 𝑣=105\;\; m/s \;\;\;\;\;\;-A\]
\[ 𝑣=29 \;\;m/s \;\;\;\;\;\;-D\]
\[ 𝑣=15\;\; m/s \;\;\;\;\;\;-B\]
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Choose the correct answer
\[3\star\star\]
Aircraft fuel is stored in a cylinder with height
\[ 82.6 \;in\]
and circumference
\[ 249 \;in\]Then the fuel volume in metric units equals
\[ v= 4.65\;\; m^3 \;\;\;\;\;\;-C\]
\[ v= 7.25 \;\;m^3\;\;\;\;\;\;-A\]
\[ v= 6.67 \;\;m^3 \;\;\;\;\;\;-D\]
\[ v= 5.42\;\; m^3 \;\;\;\;\;\;-B\]
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\[4\star\]
One of the following equations could express the position of vector
\[\vec A\]
in the figure below
\[\overrightarrow A = -2 \widehat X ,+ 3 \widehat Y ,- 2\widehat Z -C\]
\[\overrightarrow A = +2 \widehat X, - 3 \widehat Y,+ 2\widehat Z -A\]
\[\overrightarrow A = +2 \widehat X, + 3 \widehat Y, - 2\widehat Z -D\]
\[\overrightarrow A = -2 \widehat X ,+ 3 \widehat Y, + 2\widehat Z -B\]
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\[5\star\]
(A) Vector
Cartesian coordinates
\[\overrightarrow A =( +23 \widehat X , +59 \widehat Y )\] Calculate the magnitude and direction of the vector
A=63.3 , 𝜃 =68.7 0 -C
A=86.5 , 𝜃 =35.8 0 -A
A=86.5 , 𝜃 =35.8 0 -D
A=63.3 , 𝜃 =45.90 -B
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\[6\star\]
A vector with Cartesian coordinates
\[\overrightarrow A = (-3 \widehat X ,-5 \widehat Y) \]
Then it makes an angle with the positive X-axis
\[X\]with counterclockwise rotation
\[ 𝜃=239^0\;\;\;\;\;\;-C\]
\[ 𝜃=59^0\;\;\;\;\;\;-A\]
\[ 𝜃=121^0;\;\;\;\;\;-D\]
\[ 𝜃=31^0\;\;\;\;\;\;-B\]
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\[7\star \star\]
Two forces acted on a body
The components of each force are shown in
the figure below
Then the resultant of the two forces and the direction
of the resultant equals
\[\vec F_{net}=\vec F_1+\vec F_2\]
F(net)=10.8 N , 𝜃=38.8 0 -C
F(net)=6.3 N , 𝜃=54.2 0 -A
F(net)=9.5 N , 𝜃=71.6 0 -D
F(net)=8.4 N , 𝜃=28.4 0 -B
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\[8\star \star \star\]
The angle between the following two vectors
\[\overrightarrow A = \widehat X + 2 \widehat Y + 3\widehat Z \;\;\;\;\;\; \overrightarrow B = -2 \widehat X +2 \widehat Y + 2 \widehat Z \nonumber\]
is equivalent to
𝜃=310 -C
𝜃=670 -A
𝜃=260 -D
𝜃=540 -B
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Choose the correct answer
\[9\star\star\]
In the figure below, the two vectors
\[\overrightarrow A =( +5 \widehat X , +4 \widehat Y ) \;\;\;\;\;\; \overrightarrow B =( -4 \widehat X ,+2 \widehat Y ) \nonumber\]
Find the magnitude of \[ C=\vec A . \vec B=....... \]
\[ A.B=-12 \;\;\;\;\;\;-C\]
\[ A.B=12 \;\;\;\;\;\;-A\]
\[ A.B=-28\;\;\;\;\;\;-D\]
\[ A.B=28\;\;\;\;\;\;-B\]
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\[10\star \star\]
\[\overrightarrow A = +2 \widehat X + 3 \widehat Y - 2\widehat Z \;\;\;\;\;\; \overrightarrow B = -3 \widehat X +2 \widehat Y + 2 \widehat Z \nonumber\]
Find the magnitude of
\[|\vec C|= |2\vec A+3\vec B| \]
C= 18.1 -C
C=10.5 -A
C=16.3 -D
C=12.8 -B
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\[11\star\]
Three vectors with Cartesian dimensions:
\[\overrightarrow A =( +2 \widehat X , +4 \widehat Y ) \;\;\;\;\;\; \overrightarrow B =( -5 \widehat X ,+2 \widehat Y )\;\;\;\;\;\;\overrightarrow C=( 0 \widehat X , -5 \widehat Y ) \nonumber\]
shown in the figure
Based on the previous data
find the Cartesian coordinates of vector
\[\vec R\]
\[\vec R=\vec A +\vec B+\vec C\]
\[ \overrightarrow R =(-2 \widehat X , +1 \widehat Y )\;\;\;\;\;\;-C\]
\[\overrightarrow R =( +5 \widehat X , +4 \widehat Y )\;\;\;\;\;\;-A\]
\[ \overrightarrow R =( -5 \widehat X , +2 \widehat Y )\;\;\;\;\;\;-D\]
\[\overrightarrow R =( -3 \widehat X , +1 \widehat Y )\;\;\;\;\;\;-B\]
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\[12 \star\star\]
Three vectors with Cartesian dimensions:
\[\overrightarrow A =( +2 \widehat X , +4 \widehat Y ) \;\;\;\;\;\; \overrightarrow B =( -5 \widehat X ,+2 \widehat Y )\;\;\;\;\;\;\overrightarrow C=( 0 \widehat X , +5 \widehat Y ) \nonumber\]
shown in the figure
Based on the previous data
find the Cartesian coordinates of vector
\[\vec R\]
\[\vec R=\vec A -\vec B+\vec C\]
\[ \overrightarrow R =( +7 \widehat X , +7 \widehat Y ) \;\;\;\;\;\;-C\]
\[\overrightarrow R =( -7 \widehat X , -3 \widehat Y ) \;\;\;\;\;\;-A\]
\[ \overrightarrow R =( +7 \widehat X , -5 \widehat Y ) \;\;\;\;\;\;-D\]
\[\overrightarrow R =( +5 \widehat X , +4 \widehat Y ) \;\;\;\;\;\;-B\]
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\[13\star\]
A force vector
\[F=60\;\; N\]
and the vector makes an angle of \[𝜃=30^0\]
southwest. The components of the force on the perpendicular axes equal
\[ F_X=-51.96 \;\;N , F_Y= -30\;\; N \;\;\;\;\;\;-C\]
\[F_X=-45.42 \;\;N , F_Y= -18\;\; N \;\;\;\;\;\;-A\]
\[F_X=45.8 \;\;N , F_Y= 27.4\;\; N \;\;\;\;\;\;-D\]
\[F_X=35.56 \;\;N , F_Y= 18.9\;\; N\;\;\;\;\;\;-B\]
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\[14 \star\star\]
The magnitudes of the two vectors shown in the diagram below are
\[|\vec A|=6 \;\;\;\;\;\;\;\;\;\;\;\; |\vec B|=4\]Using the figure, find the magnitude and direction of vector \[\vec C=\vec A-\vec B\]
\[C= 4.3\;\; , \;\;𝜃 = -6 \;\;\;\;\;\;-C\]
\[ C= 5 \;\;,\;\; 𝜃 = 15 \;\;\;\;\;\;-A\]
\[ C= 2.42 \;\;,\;\; 𝜃 = 12 \;\;\;\;\;\;-D\]
\[C= 3.23\;\; , \;\;𝜃 = -8;\;\;\;\;\;-B\]
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\[15 \star \star \star\]
The two vectors shown below are perpendicular to each other
\[\overrightarrow A = +3 \widehat X - 2 \widehat Y - \widehat Z \;\;\;\;\;\; \overrightarrow B = -2 \widehat X -5 \widehat Y + B_z \widehat Z \nonumber\] Find the value of \[B_z\]
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Answer the following questions
[1★]
Vectors with Cartesian dimensions
shown in the figure
Based on the data in the figure below
Determine the coordinates of the vectors
\[\vec A \;\;\;\;\;\;\;\;\;\; \vec B\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
Find by drawing on the previous grid
using the vector triangle
\[\vec K= \vec A\;-\vec B\]
\[\;\;\;\;\;\;\;\;\;\;\]
The Cartesian coordinates of the two vectors
\[\vec C(4\widehat x \;, 2 \widehat y)\;\;\;\;\;\;\;\;\; \vec D(4\widehat x \;, -4 \widehat y)\]
Find using Cartesian coordinates the magnitude of the vector
\[\vec k\]
where \[\vec k=\vec C+ 2\vec D\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
Find the angle that the vector
\[\vec D\]
makes with the positive horizontal axis in a counterclockwise direction
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
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2
\[\overrightarrow A = +5 \widehat X + 2 \widehat Y \;\;\;\;\;\; \overrightarrow B = -1 \widehat X -2 \widehat Y \]
( C ) Find the magnitude
\[|\vec C|= |\vec A-2\vec B| \]
and determine the direction
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
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Point Particle Mechanics Question Bank |
Ahmed's height \[(4foot ,20 in ) \] What is Ahmed's height in meters
\[h=1.72 m \;\;\;\;\;\;-C\] |
\[ h=1.54 m \;\;\;\;\;\;-A\] |
\[h=1.81 m \;\;\;\;\;\;-D\] |
\[ h=1.62 m\;\;\;\;\;\;-B\] |
Click here to show solution
Choose the correct answer
Car speed \[65 mil/h\] Then the car speed in units of \[m/s\] equals
\[ 𝑣=82\;\; m/s \;\;\;\;\;\;-C\] |
\[ 𝑣=105\;\; m/s \;\;\;\;\;\;-A\] |
\[ 𝑣=29 \;\;m/s \;\;\;\;\;\;-D\] |
\[ 𝑣=15\;\; m/s \;\;\;\;\;\;-B\] |
Click here to show solution
Choose the correct answer
Aircraft fuel is stored in a cylinder with height \[ 82.6 \;in\] and circumference \[ 249 \;in\]Then the fuel volume in metric units equals
\[ v= 4.65\;\; m^3 \;\;\;\;\;\;-C\] |
\[ v= 7.25 \;\;m^3\;\;\;\;\;\;-A\] |
\[ v= 6.67 \;\;m^3 \;\;\;\;\;\;-D\] |
\[ v= 5.42\;\; m^3 \;\;\;\;\;\;-B\] |
Click here to show solution
Choose the correct answer
One of the following equations could express the position of vector
\[\vec A\]
in the figure below
\[\overrightarrow A = -2 \widehat X ,+ 3 \widehat Y ,- 2\widehat Z -C\] |
\[\overrightarrow A = +2 \widehat X, - 3 \widehat Y,+ 2\widehat Z -A\] |
\[\overrightarrow A = +2 \widehat X, + 3 \widehat Y, - 2\widehat Z -D\] |
\[\overrightarrow A = -2 \widehat X ,+ 3 \widehat Y, + 2\widehat Z -B\] |
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Choose the correct answer
(A) Vector
Cartesian coordinates
\[\overrightarrow A =( +23 \widehat X , +59 \widehat Y )\] Calculate the magnitude and direction of the vector
A=63.3 , 𝜃 =68.7 0 -C |
A=86.5 , 𝜃 =35.8 0 -A |
A=86.5 , 𝜃 =35.8 0 -D |
A=63.3 , 𝜃 =45.90 -B |
Click here to show solution
A vector with Cartesian coordinates \[\overrightarrow A = (-3 \widehat X ,-5 \widehat Y) \] Then it makes an angle with the positive X-axis \[X\]with counterclockwise rotation
\[ 𝜃=239^0\;\;\;\;\;\;-C\] |
\[ 𝜃=59^0\;\;\;\;\;\;-A\] |
\[ 𝜃=121^0;\;\;\;\;\;-D\] |
\[ 𝜃=31^0\;\;\;\;\;\;-B\] |
Click here to show solutionChoose the correct answer
Two forces acted on a body The components of each force are shown in the figure below Then the resultant of the two forces and the direction of the resultant equals \[\vec F_{net}=\vec F_1+\vec F_2\]
F(net)=10.8 N , 𝜃=38.8 0 -C |
F(net)=6.3 N , 𝜃=54.2 0 -A |
F(net)=9.5 N , 𝜃=71.6 0 -D |
F(net)=8.4 N , 𝜃=28.4 0 -B |
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The angle between the following two vectors \[\overrightarrow A = \widehat X + 2 \widehat Y + 3\widehat Z \;\;\;\;\;\; \overrightarrow B = -2 \widehat X +2 \widehat Y + 2 \widehat Z \nonumber\] is equivalent to
𝜃=310 -C |
𝜃=670 -A |
𝜃=260 -D |
𝜃=540 -B |
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Choose the correct answer
In the figure below, the two vectors
\[\overrightarrow A =( +5 \widehat X , +4 \widehat Y ) \;\;\;\;\;\; \overrightarrow B =( -4 \widehat X ,+2 \widehat Y ) \nonumber\]
\[ A.B=-12 \;\;\;\;\;\;-C\] |
\[ A.B=12 \;\;\;\;\;\;-A\] |
\[ A.B=-28\;\;\;\;\;\;-D\] |
\[ A.B=28\;\;\;\;\;\;-B\] |
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\[\overrightarrow A = +2 \widehat X + 3 \widehat Y - 2\widehat Z \;\;\;\;\;\; \overrightarrow B = -3 \widehat X +2 \widehat Y + 2 \widehat Z \nonumber\] Find the magnitude of \[|\vec C|= |2\vec A+3\vec B| \]
C= 18.1 -C |
C=10.5 -A |
C=16.3 -D |
C=12.8 -B |
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Choose the correct answer
Three vectors with Cartesian dimensions:
\[\overrightarrow A =( +2 \widehat X , +4 \widehat Y ) \;\;\;\;\;\; \overrightarrow B =( -5 \widehat X ,+2 \widehat Y )\;\;\;\;\;\;\overrightarrow C=( 0 \widehat X , -5 \widehat Y ) \nonumber\]
shown in the figure
Based on the previous data
find the Cartesian coordinates of vector
\[\vec R\]
\[\vec R=\vec A +\vec B+\vec C\]
\[ \overrightarrow R =(-2 \widehat X , +1 \widehat Y )\;\;\;\;\;\;-C\] |
\[\overrightarrow R =( +5 \widehat X , +4 \widehat Y )\;\;\;\;\;\;-A\] |
\[ \overrightarrow R =( -5 \widehat X , +2 \widehat Y )\;\;\;\;\;\;-D\] |
\[\overrightarrow R =( -3 \widehat X , +1 \widehat Y )\;\;\;\;\;\;-B\] |
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\[ \overrightarrow R =( +7 \widehat X , +7 \widehat Y ) \;\;\;\;\;\;-C\] |
\[\overrightarrow R =( -7 \widehat X , -3 \widehat Y ) \;\;\;\;\;\;-A\] |
\[ \overrightarrow R =( +7 \widehat X , -5 \widehat Y ) \;\;\;\;\;\;-D\] |
\[\overrightarrow R =( +5 \widehat X , +4 \widehat Y ) \;\;\;\;\;\;-B\] |
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A force vector \[F=60\;\; N\] and the vector makes an angle of \[𝜃=30^0\] southwest. The components of the force on the perpendicular axes equal
\[ F_X=-51.96 \;\;N , F_Y= -30\;\; N \;\;\;\;\;\;-C\] |
\[F_X=-45.42 \;\;N , F_Y= -18\;\; N \;\;\;\;\;\;-A\] |
\[F_X=45.8 \;\;N , F_Y= 27.4\;\; N \;\;\;\;\;\;-D\] |
\[F_X=35.56 \;\;N , F_Y= 18.9\;\; N\;\;\;\;\;\;-B\] |
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The magnitudes of the two vectors shown in the diagram below are \[|\vec A|=6 \;\;\;\;\;\;\;\;\;\;\;\; |\vec B|=4\]Using the figure, find the magnitude and direction of vector \[\vec C=\vec A-\vec B\]
\[C= 4.3\;\; , \;\;𝜃 = -6 \;\;\;\;\;\;-C\] |
\[ C= 5 \;\;,\;\; 𝜃 = 15 \;\;\;\;\;\;-A\] |
\[ C= 2.42 \;\;,\;\; 𝜃 = 12 \;\;\;\;\;\;-D\] |
\[C= 3.23\;\; , \;\;𝜃 = -8;\;\;\;\;\;-B\] |
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Choose the correct answer
The two vectors shown below are perpendicular to each other
\[\overrightarrow A = +3 \widehat X - 2 \widehat Y - \widehat Z \;\;\;\;\;\; \overrightarrow B = -2 \widehat X -5 \widehat Y + B_z \widehat Z \nonumber\] Find the value of \[B_z\]
Choose the correct answer
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Answer the following questions
Vectors with Cartesian dimensions
shown in the figure
Based on the data in the figure below
\[\overrightarrow A = +5 \widehat X + 2 \widehat Y \;\;\;\;\;\; \overrightarrow B = -1 \widehat X -2 \widehat Y \]
( C ) Find the magnitude
\[|\vec C|= |\vec A-2\vec B| \]
and determine the direction
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
Determine the coordinates of the vectors
\[\vec A \;\;\;\;\;\;\;\;\;\; \vec B\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
Find by drawing on the previous grid
using the vector triangle
\[\vec K= \vec A\;-\vec B\]
\[\;\;\;\;\;\;\;\;\;\;\]
The Cartesian coordinates of the two vectors
\[\vec C(4\widehat x \;, 2 \widehat y)\;\;\;\;\;\;\;\;\; \vec D(4\widehat x \;, -4 \widehat y)\]
Find using Cartesian coordinates the magnitude of the vector
\[\vec k\]
where \[\vec k=\vec C+ 2\vec D\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
Find the angle that the vector
\[\vec D\]
makes with the positive horizontal axis in a counterclockwise direction
\[.....................................\;\;\;\;............................................\]
\[.....................................\;\;\;\;............................................\]
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