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11.1.3.3: Problems

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    34078

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    Exercise \(\PageIndex{1}\): Rank the 5 vectors

    Five vectors are shown on the coordinate grid (position is given in meters). You can change the position of a vector by click-dragging at the base of the vector. Click restart to return the vectors to their original positions.

    1. Rank the \(x\) components of the five vectors shown (smallest to largest).
    2. Rank the \(y\) components of the five vectors shown (smallest to largest).
    3. What are the components of the vector that results when Vector B is added to Vector D?

    Problem authored by Melissa Dancy.

    Exercise \(\PageIndex{2}\): Two vectors are shown on the coordinate grid

    Two vectors are shown on the coordinate grid (position is given in meters). Restart.

    1. What are the \(x\) and \(y\) components of the blue vector?
    2. What are the \(x\) and \(y\) components of the red vector?

    Now drag the circle at the tail of the red vector so that it is on top of the blue vector's head. The vector sum is now a vector that reaches from the tail of the first (blue) vector to the head of the second (red) vector.

    1. What are the components of this vector sum?
    2. How do they relate to the components of the original (blue and red) vectors?

    Exercise \(\PageIndex{3}\): Rank the motion diagrams

    The animations represent the motion of a ball on various surfaces (position is given in meters and time is given in seconds). The "ghosts" are placed at equal time intervals. Such a picture is often called a motion diagram. Restart.

    Answer the following questions using the coordinate system specified in each animation by the red arrow. Please indicate ties by ( ). For example a suitable response could be: \(1,\: (2,\: 3),\: 4,\: 5,\: 6\).

    For parts (a), (b), and (c), use the ghost images to qualitatively rank the quantities.

    1. Rank each case from highest to lowest displacement.
    2. Rank each case from highest to lowest final velocity.
    3. Rank each case from highest to lowest acceleration (assume constant acceleration).

    Now use the usual \(x\) and \(y\) coordinates that you can access by click-dragging in the animation.

    1. Calculate the displacement vector for each animation.
    2. Calculate the acceleration vector for each animation (assume that in Animation 3 and Animation 6 the ball starts at rest and that in Animation 1 and Animation 4 the ball ends at rest).

    Problem authored by Mario Belloni*.
    *This exercise was adapted from an original Ranking Task Exercise which appears in the book Ranking Task Exercises in Physics, T. O' Kuma, D. Maloney, and C. Hieggelke.

    Exercise \(\PageIndex{4}\): A bowling ball is lifted from rest onto a shelf

    A bowling ball is lifted from rest onto a shelf by an external agent (position is given in meters and time is given in seconds). For each quantity below, rank the animations (numbered 1 through 4) from least to greatest. Ties in ( ) please. For example, a suitable response could be: \(1,\: (2,\: 3),\: 4\). Restart.

    Quantity Ranking
    magnitude of displacement  
    magnitude of average velocity  

    Table \(\PageIndex{1}\)

    Exercise \(\PageIndex{5}\): A helicopter takes off

    A flying helicopter is shown in the animation (position is given in meters and time is given in seconds). Restart.

    1. Sketch a graph of \(x\) position vs. time for the helicopter.
    2. Sketch a graph of \(y\) position vs. time for the helicopter.
    3. What is the \(x\) velocity of the helicopter at any instant?
    4. What is the \(y\) velocity of the helicopter at any instant?
    5. What is the speed of the helicopter at any instant?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{6}\): A hot-air balloon takes off

    A hot-air balloon travels as shown in the animation (position is given in meters and time is given in seconds). The \(x\) and \(y\) positions of the hot-air balloon's basket are shown in the graphs. Restart.

    1. During approximately what time interval is the magnitude of the \(y\) velocity increasing?
    2. During approximately what time interval is the magnitude of the \(y\) velocity decreasing?
    3. At approximately what instant of time does the \(y\) acceleration change from positive to negative?
    4. What is the \(y\) velocity from \(t = 87\text{ s}\) until \(t = 200\text{ s}\)?
    5. What is the \(y\) acceleration from \(t = 87\text{ s}\) until \(t = 200\text{ s}\)?
    6. What is the \(x\) velocity from \(t = 87\text{ s}\) until \(t = 200\text{ s}\)?
    7. What is the \(x\) acceleration from \(t = 87\text{ s}\) until \(t = 200\text{ s}\)?
    8. What is the \(x\) displacement from \(t = 0\text{ s}\) until \(t = 200\text{ s}\)?
    9. What is the \(y\) displacement from \(t = 0\text{ s}\) until \(t = 200\text{ s}\)?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{7}\): A projectile is launched

    A projectile is launched as shown in the animation (position is given in meters and time is given in seconds). Where does the ball reach its minimum speed, and what is its speed when it gets there? Restart.

    Exercise \(\PageIndex{8}\): Shoot the apple from the tree

    A hunter (off screen) aims his rifle at an apple in a tree as shown in the animation (position is given in meters and time is given in seconds). At the instant the bullet leaves the rifle, the apple starts falling from rest. Which of the above animations correctly depicts the hunter's aim that hits the apple?

    Note

    All three show the apple being hit, but only one animation depicts correct physics. Restart.

    Exercise \(\PageIndex{9}\): Projectile motion problem

    A projectile is launched with an initial speed of \(20\text{ m/s}\) as shown in the animation (position is given in meters). Restart. The time display is suppressed, but you can still click-drag to get coordinates. A line is also shown that represents the initial direction of the velocity.

    1. What is the launch angle?
    2. What are \(v_{0x}\) and \(v_{0y}\)?
    3. What is the maximum height the projectile will reach?
    4. How long does it take the projectile to reach that height?
    5. What is the total time that the projectile is in the air?

    Exercise \(\PageIndex{10}\): Aim the projectile to hit the moving Lamborghini

    A projectile is launched when the yellow Lamborghini (not shown to scale) goes by at \(t = 0\text{ s}\) (position is given in meters and time is given in seconds). You may change the projectile's launch angle and initial speed by using the text boxes and clicking "set values and play." Find the relationship between \(v_{0}\) and \(\theta\) such that the projectile will always hit the car. When you determine the relationship, make sure to test it with a few values of \(v_{0}\) and \(\theta\). Restart.

    Exercise \(\PageIndex{11}\): A red ball slides off a table

    A red ball slides off a table as shown in the animation (position is given in meters and time is given in seconds). Ignore air friction. If the ball collides with the other table such that \(v_{y}\) remains the same and \(v_{x}\) changes sign upon collision, where will the red ball land? Restart.

    Exercise \(\PageIndex{12}\): A basketball bounces on the floor

    A bouncing basketball is shown in the animation (position is given in meters and time is given in seconds). Restart. While the basketball is in the air, its motion is characterized by projectile motion.

    1. What is the average \(y\) acceleration of the ball during the interval of the first bounce, that is from \(t = 0.85\text{ s}\) to \(t = 0.95\text{ s}\)?
    2. What is the average \(x\) acceleration of the ball during the interval of the first bounce, that is from \(t = 0.85\text{ s}\) to \(t = 0.95\text{ s}\)?
    3. What is the magnitude of the acceleration of the ball during this interval?
    4. While the ball is in the air (between the bounces), is the \(x\) velocity increasing, decreasing, or constant? What is the \(x\) acceleration while the ball is in the air?
    5. As the ball rolls to a stop, between \(t = 3.0\text{ s}\) and \(t = 8.0\text{ s}\), what is the \(x\) acceleration of the ball? What is the \(y\) acceleration of the ball during this interval?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{13}\): A putted golf ball rolls in a straight line toward the hole

    The animation shows a putted golf ball as it travels toward the hole (position is given in meters and time is given in seconds). Restart.

    1. Is the acceleration of the golf ball between \(t = 0\) and \(t = 4.2\text{ s}\) constant, increasing, or decreasing?
    2. What is the average acceleration of the golf ball during this time interval?
    3. Calculate the \(x\) displacement of the golf ball from \(t = 0\) to \(t = 4.2\text{ s}\) and show that it is the same as what you measure on the animation.
    4. Calculate the \(y\) displacement of the golf ball from \(t = 0\) to \(t = 4.2\text{ s}\) and show that it is the same as what you measure on the animation.
    5. What is the magnitude of the displacement of the golf ball from \(t = 0\) to \(t = 4.2\text{ s}\)?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{14}\): A space probe travels with a constant acceleration

    In the animation shown, a space probe has engines that can fire on all four sides (position is given in meters and time is given in seconds). Two of the engines engage at \(t = 5\text{ s}\). Restart  The acceleration is constant and zero before the engines engage, and it is constant (but not equal to zero) after the engines engage.

    1. What is the initial velocity of the probe just before the engines fire?
    2. What is the acceleration of the probe after the engines fire?
    3. Assuming the engines continue to fire in the same way, what will be the position and velocity of the probe at \(t = 25\text{ s}\)?
    4. At what instant is \(v_{x} = 0\)? At what instant is \(v_{y} = 0\)?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{15}\): An object travels along a circular path

    An object travels along a circular path as shown in the animation (position is given in meters and time is given in seconds). Restart.

    1. At \(t = 2\text{ s}\), what is the direction of the velocity of the object?
    2. At \(t = 2\text{ s}\), what is the approximate direction of the acceleration of the object? You do not need to give an exact direction, just an approximate direction based on what you know about the direction of the radial component and the direction of the tangential component.
    3. At \(t = 4\text{ s}\), what is the direction of the velocity? If it is zero, indicate so.
    4. At \(t = 4\text{ s}\), what is the approximate direction of the acceleration? If it is zero, indicate so.
    5. At \(t = 6\text{ s}\), what is the direction of the velocity?
    6. At \(t = 6\text{ s}\), what is the approximate direction of the acceleration?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{16}\): Rotating square

    A square rotates as shown in the animation (position is given in meters and time is given in seconds). Restart. A corner of the square is labeled A. For all of the following questions consider the motion of point A from \(t = 0.5\text{ s}\) to \(t = 2.5\text{ s}\).

    1. What is the displacement of point A during this time interval?
    2. What is its distance traveled during this interval?
    3. What is its average velocity during this interval?
    4. What is its average speed during this interval?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Exercise \(\PageIndex{17}\): Uniform circular motion of a wheel

    A point (red) on a rotating wheel is shown in the animation (position given in meters and time given in seconds). Restart.

    1. What is the period of the wheel (the time it takes the red point to complete one revolution)?
    2. What is the speed of the red point?
    3. What is the magnitude of the acceleration of the red point?
    4. At \(t = 5.0\text{ s}\), what is the direction of the velocity vector and what is the direction of the acceleration vector for the red point?

    Problem authored by Aaron Titus with support by the National Science Foundation under Grant No. DUE-9952323 and placed in the public domain.

    Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.

    This page titled 11.1.3.3: Problems is shared under a CC BY-NC-ND license and was authored, remixed, and/or curated by Wolfgang Christian, Mario Belloni, Anne Cox, Melissa H. Dancy, and Aaron Titus, & Thomas M. Colbert.