In the first section of this chapter, we encouraged you to try various simulations. We call simulations where you set values and watch the results interactive problems. In this section, we explain in more detail how they work.

A sample interactive problem can be launched by clicking on the graphic on the right. When the correct x (horizontal) and y (vertical) velocities are supplied, the juggler will juggle the three balls. Before you proceed, you may wish to read the instructions below for using these interactive simulations.

As mentioned, you launch the simulations by clicking on the graphic. Typically, you will be asked to enter a value in the simulation. Sometimes you fill in a value in a text entry box, and other times you select a value using spin dials that have up and down arrow buttons.

Then, you typically push the GO button and the simulation begins − things begin to move. Most simulations have a RESET button that allows you to start again. Many have a PAUSE button that makes things go three times faster (just kidding − they pause the simulation so you can record data).

Many simulations, especially those at the beginning of the chapters, just ask you to observe how entering different values changes the results. Simulations often come with gauges that display variables as they change, such as a speedometer to keep track of a car’s speed as it goes around a track. You may observe the relationship between mass and the amount of gravitational force, for instance. Other simulations provide direct feedback if you succeed: the juggler juggles, you beat another racecar, and so forth.

Simulations later in the chapter often ask you to perform calculations in order to achieve a particular goal. These simulations are designed to make trial-and-error an ineffective tactic since they require a great amount of precision in the answer.

Enough preamble: Try the juggling simulation to the right. Enter any values you like for the initial y and x velocities, using the spin dials. Then press GO and watch as the juggler begins to juggle. Press RESET to enter a different set of values. A hint: One pair of values that will enable you to juggle is 6.0 m/s (meters per second) for the y velocity and 0.6 m/s for the x velocity.