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Incorporating a motion sensor to measure velocity and acceleration adds another dimension, as Figure 6-3 shows.
    DataStudio software displays the distance measured by the motion sensor, as shown in Figure 6-4 .
The Point
     
    When an object accelerates, its velocity changes with time. If that acceleration is constant, distance increases as the square of time.

    Figure 6-4
Position (in meters) versus time (in seconds) for three different inclines. Courtesy PASCO
.

Project 7
Independence of horizontal and vertical motion. Basketball tossed from a rolling chair .
     
The Idea
     
    Which will hit the ground first: a bullet dropped straight down from a height of 5 feet or a bullet fired horizontally over flat ground at 300 m/s from the same height? Many people guess that the greater momentum of the moving bullet would keep it in the air longer. This experiment addresses this question.
    A
projectile
is an object that has both horizontal and vertical motion. Although motion in two dimensions may seem very complicated, it can be enormously simplified based on the results of this section. You discover that the horizontal motion of a projectile is completely independent of its vertical motion. It does not matter how fast an object is falling. In this experiment, you prove this in several ways.
What You Need
     
chair
basketball
someone willing to sit in a chair
independence of horizontal and vertical motion apparatus
ballistic car
Method
     
Rolling chair
     
    This is simple to do, but it has a significant result.
Have the person sit in the chair holding the basketball.
Roll the chair (with the person sitting). The person can alternatively be on a skateboard or roller blades.
Have the person toss the basketball up and observe its trajectory.
Coins
     
     
Place a coin at the edge of a table.
Flick a second coin toward the first so that the first is just pushed over the edge and the second coin flies off the table.
Both coins should start falling at the same time. One with a horizontal velocity and one without.
Listen to see which, if any of the coins, strikes the floor first. Repeat this enough times until you get consistent results.
Apparatus
     
    Use a commercially available apparatus, such as pictured in Figures 7-1 and 7-2 . The apparatus shown in Figure 7-1 is much easier to use. The ballistics car shown in Figure 7-2 may require a level surface and some practice. A more reliable version of this is available as an accessory for an air track.

    Figure 7-1
Both balls hit the floor at the same time
.
Expected Results
     
    The basketball should go up and come down to be caught by the passenger in the rolling chair. This works best if the ball is thrown straight up in the vertical direction. Similarly, the coins will hit the ground at the same time. It is easier to compare the sound of the coins striking the floor than to make that comparison visually. When using a commercial apparatus, a greater distance from the floor gives a more definitive result.
Why It Works
     
    The force of gravity and its associated acceleration is entirely in the vertical direction. Gravity does not in any way influence the horizontal velocity.

    Figure 7-2
Ballistics car showing the steel ball has the same horizontal velocity as the car
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Other Things to Try
     
     
Place a coin at the edge of a table.
Slide a similar coin toward the first one, so the moving coin just knocks the stationary coin off the table and both fall to the floor. This will occur if the moving coin strikes the stationary coin at a large enough angle.
If a proper angle is chosen, the stationary coin is nudged off the table and falls nearly straight down. The moving coin will fall at a greater distance than the stationary coin.
The Point
     
    Horizontal motion and vertical motion are completely independent. Excluding the effects of air resistance, the horizontally fired bullet will fall to the ground at exactly the same time as the dropped bullet. This forms the basis for an