Question 1

The sum of two vectors has the greatest magnitude when the angle between these two vectors is

Accepted Answer

A) 90°. 
B) 180°. 
C) 60°. 
D) 0°. 
E) 270°. 
A) 90°. 
B) 180°. 
C) 60°. 
D) 0°. 
E) 270°. D

Question 2

A monkey is sitting at the top of a tree 20 m above ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the monkey remains seated at the top of the tree, how should the person aim the arrow containing the food so that the monkey gets the food?

Accepted Answer

A) He should aim it at the monkey. 
B) He should aim it below the monkey. 
C) He should aim it above the monkey. 
D) None of the other choices is correct. 
A) He should aim it at the monkey. 
B) He should aim it below the monkey. 
C) He should aim it above the monkey. 
D) None of the other choices is correct. C

Question 3

A hockey puck slides off the edge of a table with an initial velocity of 26.0 m/s. The height of the table above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

Accepted Answer

A) 77.2° 
B) 72.6° 
C) 12.8° 
D) 13.5° 
E) 31.8° 
A) 77.2° 
B) 72.6° 
C) 12.8° 
D) 13.5° 
E) 31.8° D

Question 4

A projectile is launched from ground level at an angle of 30.0° above horizontal with a speed of 10.0 m/s. If the projectile is moving over level ground, what is the maximum height above the ground that the projectile reaches?

Accepted Answer

A) 2.54 m 
B) 1.27 m 
C) 5.00 m 
D) 3.54 m 
E) 20.0 m 
A) 2.54 m 
B) 1.27 m 
C) 5.00 m 
D) 3.54 m 
E) 20.0 m

Question 5

Vector   is 5.5 cm long and points along the x axis. Vector   is 7.5 cm long and points at +30° above the negative x axis.
(a) Determine the x and y components of Vector   .
(b) Determine the x and y components of Vector   (c) Determine the sum of these two vectors in terms of components.
(d) Determine the sum of these two vectors in terms of magnitude and direction.

Accepted Answer

(a) A_x = 5.5 cm, A_y = 0 (b) B_x =

Question 6

Vector   = -1.00   + -2.00   and vector   = 3.00   + 4.00   . What are the magnitude and direction of vector   = 3.00   + 2.00   ?

Accepted Answer

A) 3.61 in a direction -56.3° counterclockwise from the positive x axis 
B) 3.61 in a direction 56.3° counterclockwise from the positive x axis 
C) 3.61 in a direction 33.7° counterclockwise from the positive x axis 
D) 5.00 in a direction 56.3° counterclockwise from the positive x axis 
E) 6.72 in a direction 34.4° counterclockwise from the positive x axis 
A) 3.61 in a direction -56.3° counterclockwise from the positive x axis 
B) 3.61 in a direction 56.3° counterclockwise from the positive x axis 
C) 3.61 in a direction 33.7° counterclockwise from the positive x axis 
D) 5.00 in a direction 56.3° counterclockwise from the positive x axis 
E) 6.72 in a direction 34.4° counterclockwise from the positive x axis

Question 7

If the magnitude of vector   is less than the magnitude of vector   , then the x component of   is less than the x component of   .

Accepted Answer

A) True 
 B)False

Question 8

FIGURE 3-4  
-Refer to Fig. 3-4 The magnitudes of the forces as shown in the figure are:   = 80.0 N,   = 60.0 N, and   = 40.0 N. The resultant force acting on the particle O is given by

Accepted Answer

A) 180 N at an angle 60.0° with respect to +x-axis. 
B) 60.0 N at an angle 90.0° with respect to +x-axis. 
C) 20.0 N at an angle 34.3° with respect to +x-axis. 
D) 35.5 N at an angle 34.3° with respect to +x-axis. 
E) 40.0 N at an angle 60.0° with respect to +x-axis. 
A) 180 N at an angle 60.0° with respect to +x-axis. 
B) 60.0 N at an angle 90.0° with respect to +x-axis. 
C) 20.0 N at an angle 34.3° with respect to +x-axis. 
D) 35.5 N at an angle 34.3° with respect to +x-axis. 
E) 40.0 N at an angle 60.0° with respect to +x-axis.

Question 9

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to the air to arrive at the destination?

Accepted Answer

A) 4.78° east of north 
B) 4.76° east of north 
C) 85.2° west of north 
D) 4.78° west of north 
E) 4.76° west of north 
A) 4.78° east of north 
B) 4.76° east of north 
C) 85.2° west of north 
D) 4.78° west of north 
E) 4.76° west of north

Question 10

Vector   =   +   . Under what condition is    =   +   ?

Accepted Answer

A) The statement is always true. 
B) Vectors   and
  are in perpendicular directions. 
C) The statement is never true. 
D) Vectors   and
  are in opposite directions. 
E) Vectors   and
  are in the same direction. 
A) The statement is always true. 
B) Vectors   and
  are in perpendicular directions. 
C) The statement is never true. 
D) Vectors   and
  are in opposite directions. 
E) Vectors   and
  are in the same direction.

Question 11

FIGURE 3-3  
-Vector   = 6.0 m and points 30° north of east. Vector   = 4.0 m and points 30° west of south. The resultant vector   +   is given by

Accepted Answer

A) 2.7 m at an angle 8.3° south of east. 
B) 2.7 m at an angle 8.3° east of south. 
C) 3.2 m at an angle 8.3° east of south. 
D) 3.2 m at an angle 8.3° south of east. 
E) 2.3 m at an angle 8.3° south of east. 
A) 2.7 m at an angle 8.3° south of east. 
B) 2.7 m at an angle 8.3° east of south. 
C) 3.2 m at an angle 8.3° east of south. 
D) 3.2 m at an angle 8.3° south of east. 
E) 2.3 m at an angle 8.3° south of east.

Question 12

A projectile is launched from ground level at an angle of 50.0° above horizontal with a speed of 30.0 m/s. If the projectile is moving over level ground, how long is it in the air before it again contacts the ground?

Accepted Answer

A) 8.12 s 
B) 2.35 s 
C) 4.69 s 
D) 6.44 s 
E) 11.3 s 
A) 8.12 s 
B) 2.35 s 
C) 4.69 s 
D) 6.44 s 
E) 11.3 s

Question 13

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.00 m. How far from the edge of the table, measured along the floor, does the puck hit the floor?

Accepted Answer

A) 20.0 m 
B) 40.0 m 
C) 12.8 m 
D) 19.6 m 
E) 6.4 m 
A) 20.0 m 
B) 40.0 m 
C) 12.8 m 
D) 19.6 m 
E) 6.4 m

Question 14

For a projectile launched horizontally, the horizontal component of a projectile's velocity

Accepted Answer

A) is zero. 
B) remains a non-zero constant. 
C) continuously increases. 
D) continuously decreases. 
E) any of the above, depending on position. 
A) is zero. 
B) remains a non-zero constant. 
C) continuously increases. 
D) continuously decreases. 
E) any of the above, depending on position.

Question 15

A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

Accepted Answer

A) 0.50 m/s 
B) 0.80 m/s 
C) 1.2 m/s 
D) 1.4 m/s 
E) 1.8 m/s 
A) 0.50 m/s 
B) 0.80 m/s 
C) 1.2 m/s 
D) 1.4 m/s 
E) 1.8 m/s

Question 16

The eastward component of vector   is equal to the westward component of vector   and their northward components are equal. Which one of the following statements is correct for these two vectors?

Accepted Answer

A) Vector   is parallel to vector
  . 
B) Vector   is anti-parallel to vector
  . 
C) Vector   is perpendicular to vector
  . 
D) Magnitude of vector   is equal to the magnitude of vector
  . 
E) Magnitude of vector   is twice the magnitude of vector
  . 
A) Vector   is parallel to vector
  . 
B) Vector   is anti-parallel to vector
  . 
C) Vector   is perpendicular to vector
  . 
D) Magnitude of vector   is equal to the magnitude of vector
  . 
E) Magnitude of vector   is twice the magnitude of vector
  .

Question 17

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

Accepted Answer

A) due east. 
B) due north. 
C) due south. 
D) in a southeasterly direction. 
E) in a northeasterly direction. 
A) due east. 
B) due north. 
C) due south. 
D) in a southeasterly direction. 
E) in a northeasterly direction.

Question 18

A ball is thrown at a 60.0° angle above the horizontal across level ground. It is released from a height of 2.00 m above the ground with a speed of 16.0 m/s. How long does the ball remain in the air before striking the ground?

Accepted Answer

A) 16.2 s 
B) 1.80 s 
C) 2.05 s 
D) 2.82 s 
E) 2.96 s 
A) 16.2 s 
B) 1.80 s 
C) 2.05 s 
D) 2.82 s 
E) 2.96 s

Question 19

A ball rolls off the edge of a table. The horizontal component of the ball's velocity remains constant during its entire trajectory because

Accepted Answer

A) the ball is not acted upon by any force. 
B) the net force acting on the ball is zero. 
C) the ball is not acted upon by a force in the horizontal direction. 
D) the ball is not acted upon by a force in the vertical direction. 
E) None of the other choices is correct. 
A) the ball is not acted upon by any force. 
B) the net force acting on the ball is zero. 
C) the ball is not acted upon by a force in the horizontal direction. 
D) the ball is not acted upon by a force in the vertical direction. 
E) None of the other choices is correct.

Question 20

A student adds two displacement vectors that have the magnitudes of 14.0 m and 6.0 m. What is the range of possible answers for the magnitude of the resultant vector?

Accepted Answer

between 8.

Exam 3: Kinematics in Two or Three Dimensions; Vectors

The sum of two vectors has the greatest magnitude when the angle between these two vectors is

A hockey puck slides off the edge of a table with an initial velocity of 26.0 m/s. The height of the table above the ground is 2.00 m. What is the angle below the horizontal of the velocity of the puck just before it hits the ground?

A projectile is launched from ground level at an angle of 30.0° above horizontal with a speed of 10.0 m/s. If the projectile is moving over level ground, what is the maximum height above the ground that the projectile reaches?

Vector = -1.00 + -2.00 and vector = 3.00 + 4.00 . What are the magnitude and direction of vector = 3.00 + 2.00 ?

If the magnitude of vector is less than the magnitude of vector , then the x component of is less than the x component of .

FIGURE 3-4 -Refer to Fig. 3-4 The magnitudes of the forces as shown in the figure are: = 80.0 N, = 60.0 N, and = 40.0 N. The resultant force acting on the particle O is given by

Vector = + . Under what condition is = + ?

FIGURE 3-3 -Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° west of south. The resultant vector + is given by

A projectile is launched from ground level at an angle of 50.0° above horizontal with a speed of 30.0 m/s. If the projectile is moving over level ground, how long is it in the air before it again contacts the ground?

A hockey puck slides off the edge of a table with an initial velocity of 20.0 m/s. The height of the table above the ground is 2.00 m. How far from the edge of the table, measured along the floor, does the puck hit the floor?

For a projectile launched horizontally, the horizontal component of a projectile's velocity

A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. What is the speed of the current?

The eastward component of vector is equal to the westward component of vector and their northward components are equal. Which one of the following statements is correct for these two vectors?

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

A ball is thrown at a 60.0° angle above the horizontal across level ground. It is released from a height of 2.00 m above the ground with a speed of 16.0 m/s. How long does the ball remain in the air before striking the ground?

A ball rolls off the edge of a table. The horizontal component of the ball's velocity remains constant during its entire trajectory because

A student adds two displacement vectors that have the magnitudes of 14.0 m and 6.0 m. What is the range of possible answers for the magnitude of the resultant vector?

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