Question 1

A batter hits a home run in which the ball travels 110 m horizontally with no appreciable air resistance. If the ball left the bat at 50° above the horizontal just above ground level, how fast was it hit?

Accepted Answer

The answer of A batter hits a home run in...

Question 2

Vector $\vec { A }$ has a magnitude of 6.0 m and points 30° south of east. Vector $\overrightarrow { \mathbf { B } }$ has a magnitude of 4.0 m and points 30° west of south. The resultant vector $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ is given by

Accepted Answer

A)  7.2 m at an angle of 64° south of east. 
B)  3.3 m at an angle of 64° south of east. 
C)  9.8 m at an angle of 26° south of east. 
D)  9.8 m at an angle of 64° south of east. 
E)  3.3 m at an angle of 26° south of east.

Question 3

If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude.

Accepted Answer

A) True 
 B)False

Question 4

A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

Accepted Answer

The answer of A velocity vector has components 36 m/s...

Question 5

A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?

Accepted Answer

The answer of A student adds two displacement vectors that...

Question 6

The components of vectors $\overrightarrow { \mathbf { B } }$ and $\overrightarrow { \mathrm { C } }$ are given as follows: $B _ { x }$ = -9.2 $C _ { x }$ = -4.5 $B _ { y }$ = -6.1 $C _ {  y }$ = 4.3 The angle (less than 180°) between vectors $\overrightarrow { \mathbf { B } }$ and $\overrightarrow { \mathrm { C } }$ is closest to

Accepted Answer

A)  77°. 
B)  103°. 
C)  10°. 
D)  170°. 
E)  84°.

Question 7

A celebrating student throws a water balloon horizontally from a dormitory window that is 50 m above the ground. It hits the ground at a point 60 m from the building without appreciable air resistance.
(a) What will be the horizontal component of the velocity of the balloon just before it hits the ground?
(b) What will be the magnitude of the vertical velocity of the balloon just before it hits the ground?

Accepted Answer

The answer of A celebrating student throws a water balloon...

Question 8

A displacement vector is 34.0 m in length and is directed 60.0° east of north. Selecting from the choices in the table below, what are the components of this vector?
$\begin{array}{llcc}
& \text { Northward } & \text {  } &\
  \underline{\text {  choice}} &  \underline{\text {  component}}&\underline{\text {  component}}   \
 \text { 1 } &29.4m& 17.0m  \
 \text {2  } &18.2m&28.1m\
 \text {  3} &22.4m&11.5m\
 \text {4  } &17.0m&27.4m\
 \text { 5 } &25.2m&18.2m\
\end{array}$

Accepted Answer

A)  choice 1 
B)  choice 2 
C)  choice 3 
D)  choice 4 
E)  choice 5

Question 9

Three ropes are tied in a knot as shown in the figure. One student pulls on rope A with 1.0 pound of force, and another student pulls on rope B with 7.0 pounds of force. How hard and in what direction must you pull on rope C to balance the first two pulls? Give the direction by specifying the angle (clockwise or counterclockwise) of the pull with the direction of rope A.

Accepted Answer

The answer of Three ropes are tied in a knot...

Question 10

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s2.

Accepted Answer

A)  202 m/s 
B)  9.80 m/s 
C)  19.6 m/s 
D)  45.2 m/s 
E)  94.4°

Question 11

You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

Accepted Answer

A)  directly toward the west. 
B)  directly toward the north. 
C)  in a general southwesterly direction. 
D)  in a general northwesterly direction.

Question 12

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?

Accepted Answer

A)  14 m 
B)  16 m 
C)  20 m 
D)  24 m

Question 13

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?

Accepted Answer

A)  0.160 s 
B)  0.282 s 
C)  0.313 s 
D)  0.441 s

Question 14

A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level?

Accepted Answer

A)  4.0 m/s 
B)  8.0 m/s 
C)  16 m/s 
D)  9.8 m/s

Question 15

Consider two vectors $\vec { A }$ and $\overrightarrow { \mathbf { B } }$ shown in the figure. The difference $\vec { A }$ - $\overrightarrow { \mathbf { B } }$ is best illustrated by 
(a)

(b)

(c)

(d)

Accepted Answer

A)  choice (a) 
B)  choice (b) 
C)  choice (c) 
D)  choice (d)

Question 16

A ball rolls over the edge of a platform with a horizontal velocity of magnitude v. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the magnitude of v if air resistance is negligibly small?

Accepted Answer

The answer of A ball rolls over the edge of...

Question 17

A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

Accepted Answer

A)  18.1 m/s 
B)  15.6 m/s 
C)  8.45 m/s 
D)  12.6 m/s 
E)  9.33 m/s

Question 18

Alicia intends to swim to a point straight across a 100 m wide river with a current that flows at 1.2 m/s. She can swim 2.5 m/s in still water. At what angle, measured from the upstream direction, must she swim upstream to achieve her goal?

Accepted Answer

The answer of Alicia intends to swim to a point...

Question 19

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later with no air drag.
(a) How fast was it thrown?
(b) How far from its original position did it land?
(c) How high above its original position did it go?

Accepted Answer

The answer of A projectile is thrown upward at 24°...

Question 20

A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance?

Accepted Answer

A)  6.1 m/s 
B)  7.4 m/s 
C)  8.1 m/s 
D)  8.9 m/s

Exam 3: Vectors and Motion in Two Dimensions

A batter hits a home run in which the ball travels 110 m horizontally with no appreciable air resistance. If the ball left the bat at 50° above the horizontal just above ground level, how fast was it hit?

Vector $\vec { A }$ has a magnitude of 6.0 m and points 30° south of east. Vector $\overrightarrow { \mathbf { B } }$ has a magnitude of 4.0 m and points 30° west of south. The resultant vector $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ is given by

If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude.

A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s².

You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?

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?

A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level?

A ball rolls over the edge of a platform with a horizontal velocity of magnitude v. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the magnitude of v if air resistance is negligibly small?

A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

Alicia intends to swim to a point straight across a 100 m wide river with a current that flows at 1.2 m/s. She can swim 2.5 m/s in still water. At what angle, measured from the upstream direction, must she swim upstream to achieve her goal?

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later with no air drag. (a) How fast was it thrown? (b) How far from its original position did it land? (c) How high above its original position did it go?

A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance?

Exam 3: Vectors and Motion in Two Dimensions

A batter hits a home run in which the ball travels 110 m horizontally with no appreciable air resistance. If the ball left the bat at 50° above the horizontal just above ground level, how fast was it hit?

Vector A⃗\vec { A }A has a magnitude of 6.0 m and points 30° south of east. Vector B→\overrightarrow { \mathbf { B } }B has a magnitude of 4.0 m and points 30° west of south. The resultant vector A⃗\vec { A }A + B→\overrightarrow { \mathbf { B } }B is given by

If a vector pointing upward has a positive magnitude, a vector pointing downward has a negative magnitude.

A velocity vector has components 36 m/s westward and 22 m/s northward. What are the magnitude and direction of this vector?

A student adds two displacement vectors that have the magnitudes of 12.0 m and 5.0 m. What is the range of possible answers for the magnitude of the resultant vector?

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s2.

You are trying to cross a river that flows toward the south with a strong current. You start out in your motorboat on the east bank desiring to reach the west bank directly west from your starting point. You should head your motorboat

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?

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?

A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level?

Consider two vectors A⃗\vec { A }A and B→\overrightarrow { \mathbf { B } }B shown in the figure. The difference A⃗\vec { A }A - B→\overrightarrow { \mathbf { B } }B is best illustrated by (a) (b) (c) (d)

A ball rolls over the edge of a platform with a horizontal velocity of magnitude v. The height of the platform is 1.6 m and the horizontal range of the ball from the base of the platform is 20 m. What is the magnitude of v if air resistance is negligibly small?

A boy jumps with a velocity of magnitude 20.0 m/s at an angle of 25.0° above the horizontal. What is the horizontal component of the boy's velocity?

Alicia intends to swim to a point straight across a 100 m wide river with a current that flows at 1.2 m/s. She can swim 2.5 m/s in still water. At what angle, measured from the upstream direction, must she swim upstream to achieve her goal?

A projectile is thrown upward at 24° with the vertical and returns to the horizontal ground 12.5 s later with no air drag. (a) How fast was it thrown? (b) How far from its original position did it land? (c) How high above its original position did it go?

A ball thrown horizontally from a point 24 m above the ground, strikes the ground after traveling horizontally a distance of 18 m. With what speed was it thrown, assuming negligible air resistance?

Vector $\vec { A }$ has a magnitude of 6.0 m and points 30° south of east. Vector $\overrightarrow { \mathbf { B } }$ has a magnitude of 4.0 m and points 30° west of south. The resultant vector $\vec { A }$ + $\overrightarrow { \mathbf { B } }$ is given by

A person throws a ball horizontally from the top of a building that is 24.0 m above the ground level. The ball lands 100 m down range from the base of the building. What was the initial velocity of the ball? Neglect air resistance and use g = 9.81 m/s².

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?