# Activities

• • • ##### Subject Area

• Math: Precalculus: Parametric Equations

• ##### Author 9-12

60 Minutes

• ##### Software

TI InterActive!™

• ##### Other Materials
This is Activity 8 from the EXPLORATIONS Book:
TI InterActive! Math for High School

• ##### Report an Issue

Two Dimensional Particle Motion

#### 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.

• 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