## Free Fall

3.5 Free Fall

### Learning Objectives

By the end of this section, you will be able to:

- Use the kinematic equations with the variables y and g to analyze free-fall motion.
- Describe how the values of the position, velocity, and acceleration change during a free fall.
- Solve for the position, velocity, and acceleration as functions of time when an object is in a free fall.

### Free Fall

**Practice!**

Practice 3.5.1 |
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When you drop a ball, what is true about its motion? |

(a) It falls at a speed of 9.8 m/s. |

(b) It falls and increases in speed at a rate of 9.8 m/s every second. |

(c) It falls and decreases in speed at a rate of 9.8 m/s^{2}. |

Practice 3.5.2 |
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When you throw a ball directly upward, what is true about its acceleration? |

(a) The ball’s acceleration is always directed downward. |

(b) The ball’s acceleration is always directed upward. |

(c) The ball’s acceleration is always pointed in the same direction as the ball’s motion. |

(d) The ball’s acceleration is always directed downward, except at the top of the motion, where the acceleration is zero. |

Practice 3.5.3 |
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Of the following choices, which is the best description of g? |

(a) g is gravity |

(b) g is the acceleration due to the force of gravity |

(c) g is the force of gravity |

Practice 3.5.4 |
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Which of the following velocity versus time graphs best represents the motion of throwing a ball upward and then catching it when it comes back down? |

(a) graph A |

(b) graph B |

(c) graph C |

(d) graph D |

Practice 3.5.5 |
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A ball is thrown straight upward. At the top of its trajectory, its acceleration is… |

(a) zero |

(b) straight upward |

(c) straight downward |

(d) depends on the mass of the ball |

Practice 3.5.6 |
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Instead of dropping a ball, you throw a ball directly downward. After releasing the ball, what is the magnitude of its acceleration? |

(a) Greater than 9.8 m/s^{2} |

(b) 9.8 m/s^{2} |

(c) Less than 9.8 m/s^{2} |

(d) It depends on how hard you throw the ball. |

Practice 3.5.7 |
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An object is dropped from the top of a building and hits the ground 3 s after it is released. What is the approximate speed of the object at the instant it hits the ground? |

(a) 9.8 m/s |

(b) 20 m/s |

(c) 30 m/s |

(d) 0 m/s |

Practice 3.5.8 |
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A rock is thrown downward from the top of a 40.0-m-tall tower with an initial speed of 12 m/s. Assuming negligible air resistance, what is the speed of the rock just before hitting the ground? |

(a) 0 m/s |

(b) 28 m/s |

(c) 30 m/s |

(d) 56 m/s |

(e) 784 m/s |

**Discuss!**

Consider how you would answer these questions. Then bring this to class for a group discussion.

A projectile is launched straight upward at +75.0 m/s from a height of 80.0 m, at the edge of a sheer cliff. The projectile falls, just missing the cliff and hitting the ground below.

(a) Find the maximum height of the projectile above the point of launch.

(b) Find the time it takes to hit the ground at the base of the cliff.

(c) Find its velocity at impact (include sign).

A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. When your friend, who is holding the meter stick, releases it, you react by grabbing it with those two fingers. You can calculate your reaction time from the distance the meter stick falls, read directly from the point where your fingers grabbed it.

(a) Derive a relationship for your reaction time (*t*) in terms of this measured distance (*d*).

(b) You can try this at home. If you do, just share the data you collected. If you cannot do this at home, assume the distance was 17.5 cm. Based on this distance, what is the reaction time?