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5.3. Practice Sets: Free Fall

Chapter Equations

[latex]g = \frac{\Delta v}{t} = \frac{v_f - v_i}{t}[/latex] (1)
[latex]h = \frac{v_i + v_f}{2} \times t[/latex]   (2)
[latex]h = v_i t + \frac{1}{2} a t^2[/latex]  (3)
[latex]v_{f}^2 = v_{i}^2 + 2gh_{\text{max}}[/latex]   (4)
[latex]v_i = v_f[/latex]   (5)
[latex]t_{\text{up}} = t_{\text{down}}[/latex]   (6)

Try It!

  1. A basketball player throws a ball upward from [latex]1.95 \, \text{m}[/latex] above the floor; the ball is caught by another player on its way back down, at [latex]1.50 \, \text{m}[/latex] above the floor. Which of the following statements are true:
    1. The time the ball travels upward is greater than the time it travels downward.
    2. The time the ball travels upward is equal to the time it travels downward.
    3. The time the ball travels upward is less than the time it travels downward.
  2. A child drops a toy from a bridge into the water below. This is a free-fall motion described by the following (choose the correct statement):
    1. The final velocity is zero.
    2. The initial velocity is zero.
    3. The motion is a decelerated motion (negative [latex]g[/latex]).
    4. This is a uniform motion.
  3. A student throws a book upward from floor level. The book’s round trip takes [latex]8.0 \, \text{s}[/latex] Which of the following statements are true:
    1. The initial throwing velocity cannot be calculated (there is not enough information).
    2. The time the book took to reach the maximum height is not known.
    3. The time the book took to reach the floor (on its way down) is [latex]4.0 \, \text{s}[/latex].

Practice

  1. A ball is being thrown upwards with a velocity of [latex]15 \, \text{m/s}[/latex]. Find:
    1. The maximum height the ball can reach;
    2. The time needed for the ball to reach the maximum height;
    3. The time the ball was in flight assuming it is coming back to the same level.

    Answer:

    1. [latex]11.5 \, \text{m}[/latex]
    2. [latex]1.53 \, \text{s}[/latex]
    3. [latex]3.06 \, \text{s}[/latex]
  2. A person throws a ball up in the air from the top of a [latex]25 \, \text{m}[/latex] high building. Knowing that the ball goes up in the air for [latex]12 \, \text{m}[/latex] (from the throwing point), find:
    1. The velocity of the ball at the moment it was thrown;
    2. The velocity of the ball when it reaches the ground;
    3. The time it takes the ball to reach the ground.

    Answer:

    1. [latex]15.3 \, \text{m/s}[/latex]
    2. [latex]26.9 \, \text{m/s}[/latex]
    3. [latex]4.3 \, \text{s}[/latex]
  3. A book is being dropped from the top of a [latex]3.5 \, \text{m}[/latex] high flight of stairs. Find:
    1. The velocity of the book when it reaches the ground;
    2. The time needed for the book to reach the ground.

    Answer:

    1. [latex]8.28 \, \text{m/s}[/latex]
    2. [latex]0.845 \, \text{s}[/latex]
  4. A child throws a rock from a bridge with a velocity of [latex]5.6 \, \text{m/s}[/latex]. Given that it takes the rock [latex]6.0 \, \text{s}[/latex] to reach the water underneath the bridge, how far down is the surface of the water?
    Answer:

    [latex]210 \, \text{m}[/latex]

Challenge Question(s)

An elephant taking a bath in a river is sucking water into its trunk. Suddenly, the passage of water is blocked by a rock. The elephant then turns its trunk upward and blows the water out.

Click and drag the scroll bar beneath the image below to solve the three associated questions.

Answers:

  1. [latex]1.48 \text{ s}[/latex]
  2. [latex]10.7 \text{ m}[/latex]
  3. [latex]17.4 \text{ m/s}[/latex]
Text Version of the Challenge Question(s)
  • a. If he blows the water vertically upward with a velocity of [latex]14.5 \text{ m/s}[/latex] how long will it take for the rock to reach its maximum height?
    Answer: [latex]1.48 \text{ s}[/latex]
  • b. What will be the maximum height reached by the rock?
    Answer: [latex]10.7 \text{ m}[/latex]
  • c. If the top of the elephant’s trunk in its upward position is [latex]4.7 \text{ m}[/latex] above the water level, find the speed of the rock when it reaches the surface of the water.
    Answer: [latex]17.4 \text{ m/s}[/latex]

Image Attributions

  • Challenge Question Activity:
    • “An elephant blowing water and a rock upwards” created by Juan Pablo Amorocho in the OER Lab at Centennial College

License

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College Physics – Fundamentals and Applications Copyright © by Daniela Stanescu, Centennial College is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License, except where otherwise noted.

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