Education Technology

Two Dimensional Particle Motion

Published on 06/09/2008

Activity Overview

In this activity, students explore the motion of a projectile parametrically by adjusting the projectile's initial height, initially velocity, and angle to the horizontal.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 67 - 71 from the attached PDF file for your class
  • During the Activity

    Distribute the pages to the class.

    Follow the Activity procedures:

  • Define the parametric equations for the two dimensional motion of a projectile as
    x1(t) = vo * cos(θ) * t and
    y1(t) = yo + vo * sin(θ) * t - 0.5 * 9.8 * t2
  • Define the starting position xo = 0, yo = 0, the initial velocity vo= 40 and θ = 60
  • Use the animation program to animate the path taken by a ball and plot a graph of the path
  • Find the values of the parameters of x, y, and t at maximum height from the graph and record them
  • Find the values of the parameters of x, y, and t, at the point when the ball hits the ground from the graph and record them
  • Change initial velocity to 30 and 50 and observe the effect on the parametric graph
  • Note as the initial velocity increases, the ball travels higher and further horizontally
  • Change the angle to 30 and 70 degrees, vo back to 40 and describe the effect on the graph
  • Observe that greater the value of θ, the higher the ball rises
  • Change yo to 10 and 35 degrees, θ back to 60 and describe the effect on the graph
  • Note that as the value of yo increases the graph of the object shifts up
  • After the Activity

    Students complete the Student Activity sheet.

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary