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1)  Which one of the following is an example of a vector quantity?

 

A) distance

B) velocity

C) mass

D) area

 

Answer: B

This is the only option with both magnitude and direction (vector requirements)

 

2)  Which of the following operations will not change a vector?

 

A) Translate it parallel to itself.

B) Rotate it.

C) Multiply it by a constant factor.

D) Add a constant vector to it.

 

Answer: A

A vector has magnitude and direction. Option A is the only one that does not change either

 

3)  Which of the following is an accurate statement?

 

A) A vector cannot have zero magnitude if one of its components is not zero.

B) The magnitude of a vector can be less than the magnitude of one of its components.

C) If the magnitude of vector A is less than the magnitude of vector B, then the x-component of A is less than the

      x-component of B.

D) The magnitude of a vector can be positive or negative.

 

Answer: A

If a vector is completely horizontal or vertical, making that component 0 would make the vector's magnitude 0.

 

4)  The resultant of two vectors is the smallest when the angle between them is

 

A) 0°.

B) 45°.

C) 90°.

D) 180°.

 

Answer: D

When they are opposite in direction-a subtraction results

 

5)  Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively.  When these two vectors are added, the

       magnitude of the sum

 

A) is 2.0 m.

B) could be as small as 2.0 m, or as large as 12 m.

C) is 12 m.

D) is larger than 12 m.

 

Answer: B

A and C are possible, D is impossible, B incorporates both A and C options

 

6)  Two vectors, of magnitudes 20 and 50, are added. 

       Which one of the following is a possible answer for the magnitude of the resultant?

 

A) 10

B) 20

C) 40

D) 80

 

 

Answer: C

Maximum if line in straight line (70), minimum if opposite (30).

Answer, therefore, must be from 30 to 70 including the end points. 40 is only possible answer

 

7)  Three forces, each having a magnitude of 30 N, pull on an object in directions that are 120° apart from each other. 

       Make a statement concerning the resultant force.

 

A) The resultant force is zero.

B) The resultant force is greater than 30 N.

C) The resultant force is equal to 30 N.

D) The resultant force is less than 30 N.

 

Note: N stands for a unit of force, we will cover this later

Answer: A

 

From the above figure

  the forces in the positive y direction are 2x30xsin30 = 2x30x0.5 = + 30

  the forces in the negative y direction are (just 1) = -30

  +30 - 30 = 0 

 

- 30 = 2x30x0.5 = 30 - 30 = 0

 

8)  In the diagram shown, the unknown vector is

 

                           

A)     

B)

C)

D)

 

Answer: C

By inspection, for the vector to be pointing in that direction, is by reversing the direction of A

 

9)  Ignoring air resistance, the horizontal component of a projectile's velocity

 

A) is zero.

B) remains constant.

C) continuously increases.

D) continuously decreases.

 

Answer: B

Nothing opposes the velocity so it is constant (g points down), no acceleration in x direction

Also, acceleration is defined as delta v/delta t so if acceleration is 0 then there can be no change in velocity

 

10)  A ball is thrown with a velocity of 20 m/s at an angle of 60° above the horizontal. 

         What is the horizontal component of its instantaneous velocity at the exact top of its trajectory?

 

A) 10 m/s

B) 17 m/s

C) 20 m/s

D) zero

 

Answer: A

From above, the horizontal velocity does not change

 

11)  Ignoring air resistance, the horizontal component of a projectile's acceleration

 

A) is zero.

B) remains a non-zero constant.

C) continuously increases.

D) continuously decreases.

 

Answer: A

Gravity points down, velocity does not change so acceleration is zero (also see above explanation)

 

12)  A soccer ball is kicked with a velocity of 25 m/s at an angle of 45° above the horizontal. 

         What is the vertical component of its acceleration as it travels along its trajectory?

 

A) 9.80 m/s2 downward

B) (9.80 m/s2) × sin (45°) downward

C) (9.80 m/s2) × sin (45°) upward

D) (9.80 m/s2) upward

 

Answer: A

Gravity is constant and points down

 

13)  If the acceleration vector of an object is directed anti-parallel to the velocity vector,

A) the object is turning.

B) the object is speeding up.

C) the object is slowing down.

D) the object is moving in the negative x-direction.

 

Answer: C

From definitions

 

14)  If the acceleration of an object is always directed perpendicular to its velocity,

A) the object is speeding up.

B) the object is slowing down.

C) the object is turning.

D) this situation would not be physically possible.

 

Answer: C

From definitions

 

15)  At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range?

 

A) 0°

B) 30°

C) 45°

D) 60°

 

Answer: C

See horizontal range discussion in text

 

16)  An Olympic athlete throws a javelin at four different angles above the horizontal, each with the same speed: 30°, 40°, 60°,

          and 80°.  Which two throws cause the javelin to land the same distance away?

 

A) 30° and 80°

B) 40° and 60°

C) 40° and 80°

D) 30° and 60°

 

Answer: D

See horizontal range discussion in text

 

17)  You are throwing a ball for the second time.  If the ball leaves your hand with twice the velocity it had on your first throw, its

         horizontal range R (compared to your first serve) would be

 

A) 1.4 times as much.

B) half as much.

C) twice as much.

D) four times as much.

 

Answer: D

See horizontal range discussion in text - velocity is squared

 

18)  A ball is thrown at an original speed of 8.0 m/s at an angle of 35° above the horizontal. 

          What is the speed of the ball when it returns to the same horizontal level?

 

A) 4.0 m/s

B) 8.0 m/s

C) 16 m/s

D) 9.8 m/s

 

Answer: B

Refer to previous worked problems in which ball is thrown up and then returns to hand. Also can refer to symmetry in 2-D