1. You can learn a lot by studying the plots you made from the data you took on the rocket.
- What is the velocity at the highest altitude that the rocket reached? Your answer will always be true for any body that starts moving upward near a planet's surface with only gravity acting on it. Examine your 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. Examine your 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. Try taking data with bigger "deltatime" values with all the other parameters the same (that's how you control in an experiment). Compare and find out when the computer's results aren't so reliable anymore.
3. You can take the activity apart, which is the power of Squeak. Click on the Playing button at the left for a introduction to how Squeak works, if you haven't done this already. You must click Escape Browser and your resolution must be set at 800x600 to view this properly. Go to Squeakland for tutorials and more information on using Squeak. The position of the rocket can also be calculated by equations for this case. However, you need different equations for the burn period and the freefall period. I have used that approach with a different Squeak project that you can find on my web page. It is called launch. Open that Squeak project and look at the script for the rocket and see if you can understand how it works and how it relates to what you learned about motion. Again, taking it apart and even breaking it is a good way to learn. No matter how bad a mess you make, you can always get back to the original activity by exiting Squeak and starting over, so don't worry. Explore, try what comes to your mind, and have fun exercising your brain.
4. You may think mathematics and art aren't related, but nothing could be farther from the truth. The sense of beauty you see 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 you a sense of balance and well-being in your life. 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 we challenge you to recreate the Squeak Exercise Challenge project in a way that leaves you with a sense of balance and beauty. With the tools in Squeak, you can make your 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 you will see the halo of handles. 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 you are done go to the NASA CONNECT web site to submit your version of the Squeak project and we will post it to bring beauty and balance into the lives of all who choose to open your project.