### 3.1 Kinematics in Two Dimensions: An Introduction

A ball is thrown at an angle of 45 degrees above the horizontal. Which of the following best describes the acceleration of the ball from the instant after it leaves the thrower's hand until the time it hits the ground?

- Always in the same direction as the motion, initially positive and gradually dropping to zero by the time it hits the ground
- Initially positive in the upward direction, then zero at maximum height, then negative from there until it hits the ground
- Always in the opposite direction as the motion, initially positive and gradually dropping to zero by the time it hits the ground
- Always in the downward direction with the same constant value

In an experiment, a student launches a ball with an initial horizontal velocity at an elevation 2 meters above ground. The ball follows a parabolic trajectory until it hits the ground. Which of the following accurately describes the graph of the ball's vertical acceleration versus time (taking the downward direction to be negative)?

- A negative value that does not change with time
- A gradually increasing negative value (straight line)
- An increasing rate of negative values over time (parabolic curve)
- Zero at all times since the initial motion is horizontal

A student wishes to design an experiment to show that the acceleration of an object is independent of the object's velocity. To do this, ball A is launched horizontally with some initial speed at an elevation 1.5 meters above the ground, ball B is dropped from rest 1.5 meters above the ground, and ball C is launched vertically with some initial speed at an elevation 1.5 meters above the ground. What information would the student need to collect about each ball in order to test the hypothesis?

### 3.2 Vector Addition and Subtraction: Graphical Methods

A ball is launched vertically upward. The vertical position of the ball is recorded at various points in time in the table shown.

Height (m) | Time (sec) |
---|---|

0.490 | 0.1 |

0.882 | 0.2 |

1.176 | 0.3 |

1.372 | 0.4 |

1.470 | 0.5 |

1.470 | 0.6 |

1.372 | 0.7 |

Which of the following correctly describes the graph of the ball's vertical velocity versus time?

- Always positive, steadily decreasing
- Always positive, constant
- Initially positive, steadily decreasing, becoming negative at the end
- Initially zero, steadily getting more and more negative

Height (m) | Time (sec) |
---|---|

0.490 | 0.1 |

0.882 | 0.2 |

1.176 | 0.3 |

1.372 | 0.4 |

1.470 | 0.5 |

1.470 | 0.6 |

1.372 | 0.7 |

A ball is launched at an angle of 60 degrees above the horizontal, and the vertical position of the ball is recorded at various points in time in the table shown, assuming the ball was at a height of 0 at time t = 0.

- Draw a graph of the ball's vertical velocity versus time.
- Describe the graph of the ball's horizontal velocity.
- Draw a graph of the ball's vertical acceleration versus time.

### 3.4 Projectile Motion

In an experiment, a student launches a ball with an initial horizontal velocity of 5.00 meters/sec at an elevation 2.00 meters above ground. Draw and clearly label with appropriate values and units a graph of the ball's horizontal velocity vs. time and the ball's vertical velocity vs. time. The graph should cover the motion from the instant after the ball is launched until the instant before it hits the ground. Assume the downward direction is negative for this problem.