1. Your students can learn a lot by studying the plots they made from the data they took on the rocket.

• What is the velocity at the highest altitude that the rocket reached? The answer will always be true for any body that starts moving upward near a planet's surface with only gravity acting on it. Have your students examine their plots on the Moon or other planets to check this out.
• What is the velocity of the rocket on the way down when it is at the point where there rocket engine stopped on the way up? This answer will also always be true for any body that starts moving upward near a planets surface with only gravity acting on it. Have your students examine their plots on the Moon or other planets to check this out.

These are very fundamental properties that are very useful in analyzing motion in the presence of gravity. They are worth remembering.

2. For this Squeak project, the motion of the rocket is calculated by the computer in many small steps. It doesn't use equations. If you make a small enough change in time the velocity is approximately constant so you can calculate the new position by adding the product of the current velocity and time change (change in position equals velocity times the change in time if the velocity is constant). To get the new velocity add the acceleration times the time change. Then do it again and again and again ... The computer is very good at routine tasks like this. The only problem is if you try to go too fast and make big time changes. The time change for each step is the "deltatime" at the bottom of the Control and Data Center. Have your students try taking data with bigger "deltatime" values with all the other parameters the same (that's how you control in an experiment). Then they should compare and find out when the computer's results aren't so reliable anymore.

3. This activity affords an excellent opportunity to have your students explore the interpretation of graphs and their utility in understanding concepts. The basic concepts of motion are that velocity is the change in position divided by the change in time and acceleration is the change in velocity divided by the change in time. For larger changes in time where the velocity and acceleration may be varying, they are average values over the whole time interval. As the change in time becomes smaller the velocity and acceleration approach exact values at the instant of time in question. This can be shown graphically very nicely, because the slope of the position-time curve is the velocity and the slope of the velocity-time curve is the acceleration. To get the value at a particular instant take the slope of the line tangent to the curve at that instant. By looking at their curves, students can relate the slope of points on the position-time curve, which is the velocity, to the velocity-time curve. They can check out this relationship with their data. They can also determine the acceleration from the slope of the velocity-time curve. For the case in the activity, the velocity is a positively sloping straight line for the burn period and negatively sloping straight line for the freefall period. In other words, the acceleration is constant during these intervals. Your students can measure these slopes and compare to the acceleration they entered for the burn period and the acceleration due to gravity for the freefall period. Note that the acceleration during freefall is negative as it should be because the Earth is pulling the rocket downward (we chose downward as the negative direction). By analyzing graphs, students can gain greater insight into deeper concepts. In this case they are actually exploring some of the concepts basic to calculus.

4. Your students can take the activity apart, which is the power of Squeak. Have them click on the Playing button at the left for a introduction to how Squeak works, if they haven't done this already. They must click Escape Browser and their resolution must be set at 1024x768 to view this properly. Send your students to Squeakland for tutorials and more information on using Squeak. Here are several references where you can learn more about Squeak and where to get basic information sheets to hand out to your students to guide them using Squeak. The position of the rocket can also be calculated by equations for this case. However, they will need different equations for the burn period and the freefall period. I have used that approach with a different Squeak project that they can find on my web page. It is called launch. Have your students open that Squeak project and look at the script for the rocket and see if they can understand how it works and how it relates to what they learned about motion. Again, taking it apart and even breaking it is a good way to learn. No matter how bad a mess they make, they can always get back to the original activity by exiting Squeak and starting over, so don't worry. Have your students explore, try what comes to their mind, and have fun exercising their brain.

5. It is important to foster individual aesthetic growth in your students. The sense of beauty seen in art is equally important in mathematics. Symmetry is part of beauty and it runs throughout art and mathematics. Theorems have a sense of beauty because they represent truth. Beauty gives us a sense of balance and well-being in our lives. The Squeak project was organized on the page to be functional and that often leads to a kind of beauty. But beauty is in the eye of the beholder, so challenge your students to recreate the Squeak project in a way that leaves them with a sense of balance and beauty. With the tools in Squeak, they can make their own drawings. Any of the objects can be moved and resized and their colors can often be changed. Click on any object while holding down the alt key on a PC or the command key on a Mac and a halo of handles will appear. Click on the red handle at the upper left to explore many options for changing the object. Go to Squeakland for tutorials and more information on using Squeak. When they are done go to the NASA CONNECT web site and have them submit their version of the Squeak project and we will post it to bring beauty and balance into the lives of all who choose to open their project.