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Graphs of Projectile Motion

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Lesson Focus

Graphs of Projectile Motion


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Learners create motion-time graphs and use them to analyze projectile motion.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Explain that the trajectory of a projectile is a parabola.
  • Interpret position-time graphs and velocity-time graphs.
  • Explain how the area under the velocity-time curve is used to calculate the displacement of an object.
  • Interpret and create a velocity-time graph for the horizontal and vertical components of a projectile’s motion.
  • Interpret and create a displacement-time graph for the horizontal and vertical components of a projectile’s motion.

Everything You'll Have Covered

Graphing projectile motion can deepen conceptual and mathematical understanding. Projectiles are examples of two-dimensional motion, with horizontal and vertical components. Thus, they also have x-axis components and y-axis components, respectively. Studying projectile motion requires an investigation of the relationships between gravitational acceleration, initial velocity, and angle of launch. A projectile launched at an angle follows a parabolic trajectory. Gravity and air resistance affect the trajectory of these projectiles.

In graphing projectile motion, horizontal and vertical components may be analyzed separately in terms of acceleration, velocity, and position. With two components and three variables of motion, six graphs can help to analyze projectile motion.

These graphs are:

  • Vertical acceleration vs. time;
  • Vertical velocity vs. time;
  • Vertical position vs. time;
  • Horizontal acceleration vs. time;
  • Horizontal velocity vs. time; and
  • Horizontal position vs. time.

These motion graphs are all interrelated. Applying simple ideas such as area under the curve or slope to one graph yields another graph. This is because of the mathematical interrelation of acceleration, velocity, and position. Thus, once graph (1) is sketched and analyzed, graph (2) can be sketched, and then graph (3), and so on.

Tutorial Details

Approximate Time 30 Minutes
Pre-requisite Concepts Newton’s laws of motion, sketching a graph, analyzing a graph, one-dimensional motion with constant velocity, one-dimensional motion with constant acceleration, gravity
Course Physics
Type of Tutorial Concept Development
Key Vocabulary acceleration, air resistance, angle