1.)Initiate a whole class experiment with your students taking turns throwing a ball (tennis ball, baseball, etc) from the top of stadium bleachers, or comparable situation, onto a target 15 feet away from the structure.
2.)Stategically place students into groups of 3 with different learning styles to allow for peer mentoring and tutoring. Distribute attached questionnaire. Have each group collaborate to answer the questions.
QUESTION 1: This may be an appropriate time to discuss that an object launched horizontally falls at the same rate as an object dropped. Answer: 1.37 seconds. This is determined by using the vertical position function (previously discussed.) This can be determined by solving for 't' when 4 in the final height, initial velocity is 0, and beginning height is 34. Students will need a calculator to solve the quadratic 4=16t^2+0t+34. Different methods of solving this can be discussed (square root property, quadratic formula, finding roots, etc).
QUESTION 2: Using D=rt, when D is 15ft and t is 1.37sec, students should determine r to be 10.9ft/sec.
PREDICTION: This prompt should spark a debate among groups and is the gateway to using parametric equations to follow the path of objects, in this case, our jumper.
3.)Through directed questioning, guide students to see that two equations are needed to model the path of the jumper: one to measure the distance away from the building, another to measure the distance off the ground. Now distribute the second questionnaire with the general form of the two parametric equations to follow the paths of objects launched on this planet. A connection can be made to Earth Science on the gravitational pulls of other planets and our moon.
4.)Students will collaborate to answer the first question.
1. x=5.45ft y=27.44ft
2. To follow the path of the object, students will need to change modes of their graphing utility from function to parametric mode. Students can use the trace feature or other methods to determine if they will land in the net.
Students who do not have graphing calculators can access one at the website linked below.
EXPLORATION: By substituting 15 for x and 4 for y, students will notice that two variables are missing: t & v. Students can solve this system of equations by substitution. ( Graphing Calculator) This Illuminations website has a functioning graphing calculator.
5.)Show students the video of the ball tosses and facilitate a whole group discussion on adjustments that would need to be made for each throw to hit the target.
6.)Close the lesson by having the students create their own story in which parametric equations must be used to achieve a happy (or sad) ending for homework.
