Is Horizontal Motion of a Projectile Independent From its Vertical Motion?

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.

1. Have the person sit in the chair holding the basketball.
2. Roll the chair (with the person sitting). The person can alternatively be on a skateboard or roller blades.
3. Have the person toss the basketball up and observe its trajectory.

Coins

1. Place a coin at the edge of a table.
2. 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.
3. Both coins should start falling at the same time. One with a horizontal velocity and one without.
4. 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.

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.

Other Things to Try

1. Place a coin at the edge of a table.
2. 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.
3. 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 understanding of projectile motion that is greatly simplified by treating the vertical and horizontal motion separately, as if the other did not even exist.

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