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Applying the science practices: independence of horizontal and vertical motion or maximum height and flight time

Choose one of the following experiments to design:

Design an experiment to confirm what is shown in Figure 3.6 , that the vertical motion of the two balls is independent of the horizontal motion. As you think about your experiment, consider the following questions:

  • How will you measure the horizontal and vertical positions of each ball over time? What equipment will this require?
  • How will you measure the time interval between each of your position measurements? What equipment will this require?
  • If you were to create separate graphs of the horizontal velocity for each ball versus time, what do you predict it would look like? Explain.
  • If you were to compare graphs of the vertical velocity for each ball versus time, what do you predict it would look like? Explain.
  • If there is a significant amount of air resistance, how will that affect each of your graphs?

Design a two-dimensional ballistic motion experiment that demonstrates the relationship between the maximum height reached by an object and the object's time of flight. As you think about your experiment, consider the following questions:

  • How will you measure the maximum height reached by your object?
  • How can you take advantage of the symmetry of an object in ballistic motion launched from ground level, reaching maximum height, and returning to ground level?
  • Will it make a difference if your object has no horizontal component to its velocity? Explain.
  • Will you need to measure the time at multiple different positions? Why or why not?
  • Predict what a graph of travel time versus maximum height will look like. Will it be linear? Parabolic? Horizontal? Explain the shape of your predicted graph qualitatively or quantitatively.
  • If there is a significant amount of air resistance, how will that affect your measurements and your results?

It is remarkable that for each flash of the strobe, the vertical positions of the two balls are the same. This similarity implies that the vertical motion is independent of whether or not the ball is moving horizontally. (Assuming no air resistance, the vertical motion of a falling object is influenced by gravity only, and not by any horizontal forces.) Careful examination of the ball thrown horizontally shows that it travels the same horizontal distance between flashes. This is due to the fact that there are no additional forces on the ball in the horizontal direction after it is thrown. This result means that the horizontal velocity is constant, and affected neither by vertical motion nor by gravity (which is vertical). Note that this case is true only for ideal conditions. In the real world, air resistance will affect the speed of the balls in both directions.

The two-dimensional curved path of the horizontally thrown ball is composed of two independent one-dimensional motions (horizontal and vertical). The key to analyzing such motion, called projectile motion , is to resolve (break) it into motions along perpendicular directions. Resolving two-dimensional motion into perpendicular components is possible because the components are independent. We shall see how to resolve vectors in Vector Addition and Subtraction: Graphical Methods and Vector Addition and Subtraction: Analytical Methods . We will find such techniques to be useful in many areas of physics.

Phet explorations: ladybug motion 2d

Learn about position, velocity and acceleration vectors. Move the ladybug by setting the position, velocity or acceleration, and see how the vectors change. Choose linear, circular or elliptical motion, and record and playback the motion to analyze the behavior.

Ladybug Motion 2D

Test prep for ap courses

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?

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

(d)

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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)?

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

We would need to know the horizontal and vertical positions of each ball at several times. From that data, we could deduce the velocities over several time intervals and also the accelerations (both horizontal and vertical) for each ball over several time intervals.

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Summary

  • The shortest path between any two points is a straight line. In two dimensions, this path can be represented by a vector with horizontal and vertical components.
  • The horizontal and vertical components of a vector are independent of one another. Motion in the horizontal direction does not affect motion in the vertical direction, and vice versa.

Questions & Answers

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Practice Key Terms 1

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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