Wednesday, November 21, 2012

Dropping Objects From The Tips Of Your Toes: Quadratics

How long would it take a ball to drop to the ground if you reached as far up as possible? Let's find out with some help from quadratics and the square root property.

What You Will Need

  • Golf balls, tennis balls, etc
  • Stopwatch
  • Measuring tape
  • Formula for acceleration due to gravity neglecting air resistance.
  • Activity sheet

Overview and Goal of Activity

The goal of this exercise is for students to use algebra to solve a real-life application. Students will work in pairs (or groups depending on the amount of stop watches you have at your disposal) to calculate how long a small ball will take to fall from the tips of their toes, reaching as high as possible, to the ground. Students will first use algebra and then will test their answer by actually timing the fall


Step 1: Using adhesive or tape, tape at least one tape-measure to the wall from the floor to the ceiling.
Step 2: Pair up students and give each group a stop watch and an activity sheet (below)
Step 3: Have students measure themselves in inches or centimeters and record their height—Make sure they are measuring from the tips of their toes to their finger tips while reaching to the ceiling.
Step 4: Next, using the formula s(t) = 16t^2, where t is their height in seconds have them plug in their height for s(t).
Step 5: Have students do their best to solve for t.
Step 6: Have the students record their answer
Step 7: Have students go back to their seats
Step 8: Explain the process of how to solve for t by using the square root property.
Step 9: Have them partner back up and solve for t and record their answer
Step 10: Have students test their answer by dropping a ball and timing it. Have them record their answer
Step 11: Back to their seats for after activity discussion

Example of Activity Sheet

1) How tall are you from your toes to your finger tips __________cm/inches

Formula for acceleration due to gravity is
s(t) = 16t^2

2) Plug in your height for s(t) and do you best to solve for t

t = ___________

3) Notes from your teacher about how to solve

4) Using your notes from above, plug in your height for s(t) and solve for t

s(t) = 16t^2

t = __________

5): Using your stop watch take turns dropping the ball from the tips of your toes and record you answer (do this at least twice).

Time for ball to hit the ground ___________seconds

After Activity Discussion:

How close was your stop watch recording to your solution?
Why do you think there might be a difference in the times?
What does the s(t) stand for in the equation?
What does the 16^2 stand for?
Why do you think the 16 is squared?
Do you think your time would be different if you dropped a heavy rock instead of the ball?
Do you think your time would be different if you dropped a leaf?
Why are there two answers?
Why do we ignore the minus in our two answers?


Perform the same experiment with your mom, dad, sister or brother

Actual Problem Worked Out

Height = 84inches

84 = 16t^2
84/16 = t^2
21/4 = t^2
+/-squar root (21/4) = t
t= +/-2.29 seconds
t = 2.29seconds


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