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

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) = v_{o} * cos(θ) * t and y1(t) = y_{o} + v_{o} * sin(θ) * t - 0.5 * 9.8 * t^{2}

Define the starting position x_{o} = 0, y_{o} = 0, the initial velocity v_{o}= 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, v_{o} back to 40 and describe the effect on the graph

Observe that greater the value of θ, the higher the ball rises

Change y_{o} to 10 and 35 degrees, θ back to 60 and describe the effect on the graph

Note that as the value of y_{o} 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