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1. Which of the following statements are true of scalars and vectors? List all that are TRUE.

- A vector quantity always has a direction associated with it.
- A scalar quantity can bave a direction associated with it.
- Vectors can be added together; scalar quantites cannot.
- Vectors can be represented by an arrow on a scaled diagram; the length of the arrow represents the vector's magnitude and the direction it points represents the vector's direction.

a. b. c. d. |

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Scalars and Vectors || Vectors and Direction |

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2. Which of the following quantities are vectors? Include all that apply.

- distance traveled
- displacement
- average speed
- average velocity
- instantaneous velocity
- acceleration

Of the five kinematic quantities listed here (distance, displacement, speed, velocity and acceleration), three of them are vectors. Displacement, velocity (both average and instantaneous), and acceleration all require the mention of a direction in order to fully describe the quantity. |

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Scalars and Vectors |

3. Numerical values and directions are stated for a variety of quantities. Which of these statements represent a vector description? Include all that apply.

- 20 meters, west
- 9.8 m/s/s
- 35 mi/hr, south
- 16 years old
- 60 minutes
- 3.5 m/s/s, south
- -3.5 m/s/s
- +20 degrees C

Expressions of vector
quantities would include a magnitude (number, value, etc.) and a
direction. The direction could be described as being north, south,
east, west or left, right, up, down. On occasion, a "+" or "-" is used
to describe the direction. Since mathematical computations on
calculators do not fare well with the typing of "south," a - sign is
often substituted for a given direction. In the case of |

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Scalars and Vectors |

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4. Which of the following statements are true of vector addition, vector subtraction, and vector addition diagrams? List all that apply.

- Vectors A, B, and C are added together as A + B + C. If the order in which they are added is changed to C + B + A, then the result would be different.
- Vectors A, B, and C are added together as A + B + C. If the order in which they are added is reversed to C + B + A, then the result would be a vector with the same magnitude but the opposite direction.
- When constructing a vector diagram for A + B + C, it is not absolutely necessary that vectors B and C use the same scale that is used by vector A.
- The resultant in a vector addition diagram always extends from the head of the last vector to the tail of the first vector.
- If vectors A and B are added at right angles to each other, then one can be sure that the resultant will have a magnitude that is greater than the magnitudes of either one of the individual vectors A and B.
- If vectors A and B are added at right angles to each other, then one can be sure that the resultant will have a magnitude that is less than the arithmetic sum of the magnitudes of A and B.
- Vector addition diagrams cannot be used to determine the resultant when there is a vector subtraction operation.

a. b. c. d. e. f. g. |

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Vector Addition || Resultants |

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5. Which of the following descriptions of moving objects accurately portray a projectile? List all that apply.

- an object which is moving through the air and not touching any surface
- a falling skydiver with an open parachute
- any object upon which air resistance is negligible
- a free-falling object
- an object upon which the only significant force is the force of gravity
- a falling feather
- a falling feather in a vacuum chamber
- a falling feather in a falling vacuum chamber.

A projectile is an object upon which the only force is gravity. Air resistance must be negligible or nonexistent. Other forces resulting from people or things pulling or pushing, attached strings or contact with surfaces must not be present. a. b. c. d. e. f. g. h. |

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What is a Projectile? |

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6. Which of the following statements are true of projectiles? List all that apply.

- A projectile is a free-falling object.
- A projectile experiences negligible or no air resistance.
- A projectile must be moving in the downward direction.
- A projectile must be accelerating in the downward direction.
- A projectile does not have to have horizontal motion.
- A projectile could begin its projectile motion with a downward velocity.
- A projectile does not need to be "falling."

a. b. c. d. e. f. g. |

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What is a Projectile? || Characteristics of a Projectile's Trajectory |

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7. Which of the following statements are true of the horizontal motion of projectiles? List all that apply.

- A projectile does not have a horizontal velocity.
- A projectile with a rightward component of motion will have a rightward component of acceleration.
- The horizontal velocity of a projectile changes by 9.8 m/s each second.
- A projectile with a horizontal component of motion will have a constant horizontal velocity.
- The horizontal velocity of a projectile is 0 m/s at the peak of its trajectory.
- The horizontal velocity of a projectile is unaffected by the vertical velocity; these two components of motion are independent of each other.
- The horizontal displacement of a projectile is dependent upon the time of flight and the initial horizontal velocity.
- The final horizontal velocity of a projectile is always equal to the initial horizontal velocity.
- As a projectile rises towards the peak of its trajectory, the horizontal velocity will decrease; as it falls from the peak of its trajectory, its horizontal velocity will decrease.
- Consider a projectile launched from ground level at a fixed
launch speed and a variable angle and landing at ground level. The
horizontal displacement (i.e., the
*range*) of the projectile will always increase as the angle of launch is increased from 0 degrees to 90 degrees. - Consider a projectile launched from ground level at a fixed
launch angle and a variable launch speed and landing at ground level.
The horizontal displacement (i.e., the
*range*) of the projectile will always increase as the launch speed is increased.

a. b. c. d. e. f. g. h. i. j. k. |

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Characteristics of a Projectile's Trajectory || Horizontal and Vertical Components of Velocity || Horizontal and Vertical Components of Displacement |

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8. Which of the following statements are true of the vertical motion of projectiles? List all that apply.

- The vertical component of a projectile's velocity is a constant value of 9.8 m/s.
- The vertical component of a projectile's velocity is constant.
- The vertical component of a projectile's velocity is changing.
- The vertical component of a projectile's velocity is changing at a constant rate.
- A projectile with an upward component of motion will have a upward component of acceleration.
- A projectile with an downward component of motion will have a downward component of acceleration.
- The magnitude of the vertical velocity of a projectile changes by 9.8 m/s each second.
- The vertical velocity of a projectile is 0 m/s at the peak of its trajectory.
- The vertical velocity of a projectile is unaffected by the horizontal velocity; these two components of motion are independent of each other.
- The final vertical velocity of a projectile is always equal to the initial vertical velocity.
- The vertical acceleration of a projectile is 0 m/s/s when it is at the peak of its trajectory.
- As a projectile rises towards the peak of its trajectory, the vertical acceleration will decrease; as it falls from the peak of its trajectory, its vertical acceleration will decrease.
- As a projectile rises towards the peak of its trajectory, the vertical acceleration is directed upward; as it falls from the peak of its trajectory, its vertical acceleration is directed downward.
- The peak height to which a projectile rises above the launch location is dependent upon the initial vertical velocity.
- As a projectile rises towards the peak of its trajectory, the vertical velocity will decrease; as it falls from the peak of its trajectory, its vertical velocity will decrease.
- Consider a projectile launched from ground level at a fixed
launch speed and a variable angle and landing at ground level. The
vertical displacement of the projectile during the first half of its
trajectory (i.e., the
*peak height*) will always increase as the angle of launch is increased from 0 degrees to 90 degrees. - Consider a projectile launched from ground level at a fixed
launch angle and a variable launch speed and landing at ground level.
The vertical displacement of the projectile during the first half of
its trajectory (i.e., the
*peak height*) will always increase as the launch speed is increased.

a. b. c. d. e. f. g. h. i. j. k. l. m. n. o. p. q. |

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Characteristics of a Projectile's Trajectory || Horizontal and Vertical Components of Velocity || Horizontal and Vertical Components of Displacement |

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9. Which of the following statements are true of the time of flight for a projectile? List all that apply.

- The time that a projectile is in the air is dependent upon the horizontal component of the initial velocity.
- The time that a projectile is in the air is dependent upon the vertical component of the initial velocity.
- For a projectile which lands at the same height that it is projected from, the time to rise to the peak is equal to the time to fall from its peak to the original height.
- For the same upward launch angles, projectiles will stay in the air longer if the initial velocity is increased.
- Assume that a kicked ball in football is a projectile. If the ball takes 3 seconds to rise to the peak of its trajectory, then it will take 6 seconds to fall from the peak of its trajectory to the ground.

a. b. c. d. e. |

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Characteristics of a Projectile's Trajectory || Horizontal and Vertical Components of Velocity || Horizontal and Vertical Components of Displacement |

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