Question 1

A rock is thrown from the roof of a building, with an initial velocity of 10 m/s at an angle of 30° above the horizontal. The rock is observed to strike the ground 43 m from the base of the building. What is the height of the building assuming no air resistance?

Accepted Answer

The answer of A rock is thrown from the roof...

Question 2

A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector?

Accepted Answer

A)  0 km
B)  20 km
C)  28 km
D)  40 kmE) A) and D)
F) All of the above

Question 3

The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.

Accepted Answer

A) True 
 B)False

Question 4

A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance,

Accepted Answer

A)  its range will be increased by  2\sqrt { 2 }2c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​  .
B)  its range will double.
C)  its range will be decreased by a factor of two.
D)  its range will quadruple.
E)  its range will decrease by a factor of four. F) A) and E)
G) A) and D)

Question 5

A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground. At what angle below the horizontal does the ball approach the ground?

Accepted Answer

A)  35°
B)  42°
C)  48°
D)  40°
E)  65°F) A) and D)
G) A) and C)

Question 6

Vector  A→\overrightarrow { \mathrm { A } }A  has a magnitude of 7.0 m and points 30° east of north. Vector  B→\overrightarrow { \mathrm { B } }B  has a magnitude of 5.0 m and points 30° west of south. The resultant vector  A→\overrightarrow { \mathrm { A } }A  +  B→\overrightarrow { \mathrm { B } }B  is given by

Accepted Answer

A)  10.0 m at an angle 60° north of east.
B)  10.0 m at an angle 30° east of north.
C)  2.0 m at an angle 30° north of east.
D)  2.0 m at an angle 60° north of east.
E)  1.0 m at an angle 60° east of north F) B) and C)
G) A) and E)

Question 7

A cat leaps to try to catch a bird. If the cat's jump was at 60° off the ground and its initial velocity was  2.74 m/s2.74 \mathrm {~m} / \mathrm { s }2.74 m/s  what is the highest point of its trajectory, neglecting air resistance?

Accepted Answer

A)  0.29 m
B)  0.58 m
C)  10.96 m
D)  0.19 m E) All of the above
F) None of the above

Question 8

A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?

Accepted Answer

A)  It is impossible to tell because we do not know their masses.
B)  the stone
C)  the ball
D)  Both are traveling at the same speed.E) A) and B)
F) None of the above

Question 9

If three vectors add to zero, they must all have equal magnitudes.

Accepted Answer

A) True 
 B)False

Question 10

A vector $\overrightarrow { \mathrm { A } }$ has components Ax = 12.0 m and Ay = 5.00 m.
(a)What is the angle that vector $\overrightarrow { \mathrm { A } }$ makes with the +x-axis?
(b)What is the magnitude of vector $\overrightarrow { \mathrm { A } }$ ?

Accepted Answer

Question 11

A boy throws a rock with an initial velocity of  3.13 m/s3.13 \mathrm {~m} / \mathrm { s }3.13 m/s  at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s2?

Accepted Answer

A)  0.160 s
B)  0.282 s
C)  0.313 s
D)  0.441 s E) A) and D)
F) A) and C)

Question 12

A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal. What is the vertical component of its velocity after 4.0 s if air resistance is neglected?

Accepted Answer

A)  150 m/s
B)  36 m/s
C)  130 m/s
D)  75 m/s
E)  38 m/sF) C) and D)
G) A) and E)

Question 13

Three vectors,  S→\overrightarrow { \mathrm { S } }S  ,  T→\overrightarrow { \mathbf { T } }T  , and  U→\overrightarrow { \mathrm { U } }U  , have the components shown in the table. What angle does the resultant of these three vectors make with the +x-axis?  x component y component s→−3.5 m4.5 mT→0.00 m−6.5 mU→5.5 m−2.5 m\begin{array}{|c|c|c|}\hline & x 	ext { component } & y 	ext { component } \\hline \begin{array}{c}\overrightarrow{\mathrm{s}} \\end{array} & -3.5 \mathrm{~m} & 4.5 \mathrm{~m} \\hline \begin{array}{c}\overrightarrow{\mathrm{T}} \\end{array} & 0.00 \mathrm{~m} & -6.5 \mathrm{~m} \\hline \begin{array}{c}\overrightarrow{\mathrm{U}} \\end{array} & 5.5 \mathrm{~m} & -2.5 \mathrm{~m} \\hline\end{array}s​T​U​​x component −3.5 m0.00 m5.5 m​y component 4.5 m−6.5 m−2.5 m​​

Accepted Answer

A)  24° above the +x-axis
B)  24° below the +x-axis
C)  66° above the +x-axis
D)  66° below the +x-axis E) A) and B)
F) None of the above

Question 14

A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter. What is the magnitude of the acceleration of the car?

Accepted Answer

A)  0 m/s2
B)  1.0 m/s2
C)  10 m/s2
D)  0.63 m/s2
E)  2.2 m/s2F) B) and C)
G) A) and B)

Question 15

If a vector's components are all negative, then the magnitude of the vector is negative.

Accepted Answer

A) True 
 B)False

Question 16

A hockey puck slides off the edge of a horizontal platform with an initial velocity of 20 m/s horizontally and experiences no significant air resistance. The height of the platform above the ground is 2.0 m. What is the magnitude of the vertical component of the velocity of the puck just before it hits the ground?

Accepted Answer

A)  20 m/s
B)  6.3 m/s
C)  13 m/s
D)  15 m/s
E)  21 m/sF) C) and E)
G) A) and C)

Question 17

The driver of a motorboat that can move at 10 m/s in still water wishes to travel directly across a river in which the current flows at 5.0 m/s.
(a)At what angle, measured from the upstream direction, should the driver head the boat?
(b)How many minutes will it take to cross the river if it is 1.6 km wide at that point?

Accepted Answer

The answer of The driver of a motorboat that can...

Question 18

The eastward component of vector  A→\overrightarrow { \mathrm { A } }A  is equal to the westward component of vector  B→\overrightarrow { \mathrm { B } }B  and their northward components are equal. Which one of the following statements must be correct for these two vectors?

Accepted Answer

A)  Vector  A→\overrightarrow { \mathrm { A } }A-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  is parallel to vector  B→\overrightarrow { \mathrm { B } }B-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  .
B)  Vector  A→\overrightarrow { \mathrm { A } }A-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  is antiparallel (in the opposite direction) to vector  B→\overrightarrow { \mathrm { B } }B-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  .
C)  Vector  A→\overrightarrow { \mathrm { A } }A-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  must be perpendicular to vector  B→\overrightarrow { \mathrm { B } }B-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  .
D)  The magnitude of vector  A→\overrightarrow { \mathrm { A } }A-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  must be equal to the magnitude of vector  B→\overrightarrow { \mathrm { B } }B-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  .
E)  The angle between vector  A→\overrightarrow { \mathrm { A } }A-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  and vector  B→\overrightarrow { \mathrm { B } }B-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/>  must be 90°. F) A) and B)
G) B) and E)

Question 19

The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to

Accepted Answer

A)  19
B)  16
C)  13
D)  10
E)  7.0F) C) and E)
G) C) and D)

Question 20

A hunter points a rifle horizontally and holds it 3.30 m above the ground. The bullet leaves the barrel at 325 m/s and experiences no significant air resistance. The acceleration due to gravity at this location is 9.80 m/s2.
(a)How long does it take for the bullet to strike the ground?
(b)How far horizontally does it travel?

Accepted Answer

Exam 3: Vectors and Motion in Two Dimensions

A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance,

Correct Answer
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A cat leaps to try to catch a bird. If the cat's jump was at 60° off the ground and its initial velocity was $2.74 \mathrm {~m} / \mathrm { s }$ what is the highest point of its trajectory, neglecting air resistance?

Correct Answer
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A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter. What is the magnitude of the acceleration of the car?

Correct Answer
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The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to

Correct Answer
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Correct Answer
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If three vectors add to zero, they must all have equal magnitudes.

Correct Answer
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If a vector's components are all negative, then the magnitude of the vector is negative.

Correct Answer
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A rock is thrown from the roof of a building, with an initial velocity of 10 m/s at an angle of 30° above the horizontal. The rock is observed to strike the ground 43 m from the base of the building. What is the height of the building assuming no air resistance?

Correct Answer
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A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground. At what angle below the horizontal does the ball approach the ground?

Correct Answer
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Correct Answer
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A vector $\overrightarrow { \mathrm { A } }$ has components A_x = 12.0 m and A_y= 5.00 m. (a)What is the angle that vector $\overrightarrow { \mathrm { A } }$ makes with the +x-axis? (b)What is the magnitude of vector $\overrightarrow { \mathrm { A } }$ ?

Correct Answer
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A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal. What is the vertical component of its velocity after 4.0 s if air resistance is neglected?

Correct Answer
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Correct Answer
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A boy throws a rock with an initial velocity of $3.13 \mathrm {~m} / \mathrm { s }$ at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s²?

Correct Answer
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The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.

Correct Answer
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Correct Answer
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The eastward component of vector $\overrightarrow { \mathrm { A } }$ is equal to the westward component of vector $\overrightarrow { \mathrm { B } }$ and their northward components are equal. Which one of the following statements must be correct for these two vectors?

Correct Answer
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Correct Answer
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A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector?

Correct Answer
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A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?

Correct Answer
verified

Exam 3: Vectors and Motion in Two Dimensions

A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance,

Correct AnswerverifiedShow Answer

A cat leaps to try to catch a bird. If the cat's jump was at 60° off the ground and its initial velocity was 2.74 m/s2.74 \mathrm {~m} / \mathrm { s }2.74 m/s what is the highest point of its trajectory, neglecting air resistance?

Correct AnswerverifiedShow Answer

A race car traveling at a constant speed of 50 m/s drives around a circular track that is 500 m in diameter. What is the magnitude of the acceleration of the car?

Correct AnswerverifiedShow Answer

The figure shows three vectors and their magnitudes and relative directions. The magnitude of the resultant of the three vectors is closest to

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

If three vectors add to zero, they must all have equal magnitudes.

Correct AnswerverifiedShow Answer

If a vector's components are all negative, then the magnitude of the vector is negative.

Correct AnswerverifiedShow Answer

A rock is thrown from the roof of a building, with an initial velocity of 10 m/s at an angle of 30° above the horizontal. The rock is observed to strike the ground 43 m from the base of the building. What is the height of the building assuming no air resistance?

Correct AnswerverifiedShow Answer

A child throws a ball with an initial speed of 8.0 m/s at an angle of 40° above the horizontal. The ball leaves her hand 1.0 m above the ground. At what angle below the horizontal does the ball approach the ground?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A vector A→\overrightarrow { \mathrm { A } }A has components Ax = 12.0 m and Ay = 5.00 m. (a)What is the angle that vector A→\overrightarrow { \mathrm { A } }A makes with the +x-axis? (b)What is the magnitude of vector A→\overrightarrow { \mathrm { A } }A ?

Correct AnswerverifiedShow Answer

A high-speed dart is shot from ground level with a speed of 150 m/s at an angle 30° above the horizontal. What is the vertical component of its velocity after 4.0 s if air resistance is neglected?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A boy throws a rock with an initial velocity of 3.13 m/s3.13 \mathrm {~m} / \mathrm { s }3.13 m/s at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s2?

Correct AnswerverifiedShow Answer

The magnitude of the resultant of two vectors cannot be less than the magnitude of either of those two vectors.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

The eastward component of vector A→\overrightarrow { \mathrm { A } }A is equal to the westward component of vector B→\overrightarrow { \mathrm { B } }B and their northward components are equal. Which one of the following statements must be correct for these two vectors?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A car travels 20 km west and then 20 km south. What is the magnitude of its displacement vector?

Correct AnswerverifiedShow Answer

A ball is thrown horizontally from the top of a tower at the same instant that a stone is dropped vertically. Which object is traveling faster when it hits the level ground below if neither of them experiences any air resistance?

Correct AnswerverifiedShow Answer

Correct Answer
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A cat leaps to try to catch a bird. If the cat's jump was at 60° off the ground and its initial velocity was $2.74 \mathrm {~m} / \mathrm { s }$ what is the highest point of its trajectory, neglecting air resistance?

Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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Correct Answer
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A vector $\overrightarrow { \mathrm { A } }$ has components A_x = 12.0 m and A_y= 5.00 m. (a)What is the angle that vector $\overrightarrow { \mathrm { A } }$ makes with the +x-axis? (b)What is the magnitude of vector $\overrightarrow { \mathrm { A } }$ ?

Correct Answer
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Correct Answer
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A boy throws a rock with an initial velocity of $3.13 \mathrm {~m} / \mathrm { s }$ at 30.0° above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory if air resistance is negligibly small and g = 9.80 m/s²?

Correct Answer
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Correct Answer
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Correct Answer
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The eastward component of vector $\overrightarrow { \mathrm { A } }$ is equal to the westward component of vector $\overrightarrow { \mathrm { B } }$ and their northward components are equal. Which one of the following statements must be correct for these two vectors?

Correct Answer
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Correct Answer
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Correct Answer
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