Horizontal and Vertical Motion

Problem:

How do the vertical and horizontal motions of a projectile affect one another?

Which hits the ground first: a bullet fired horizontally from a gun or a bullet dropped from the same height as the gun?

Materials

• Chair
• Skateboard
• Soccer ball or basketball
• A friend or volunteer
• Smooth floor
• Table
• Two coins
• Manila folder (or a thin piece of cardboard—something that is rigid but can be folded)

Procedure

Skateboard

1. Have your friend or volunteer stand or sit on the skateboard while holding the ball.
2. Roll the skateboard forward.
3. While rolling, have the person on the skateboard toss the ball straight up into the air. Observe the ball’s trajectory. Where does it go? Is the person able to catch the ball on its descent?

Coins

1. Cut the folder into a square roughly 5 inches on a side.
2. Fold the square to make a 2-inch wide “flap”. Position the flap so that it sticks straight up and down.
3. Place the square on the corner of a table so that the two corners stick out from both table edges. One on side, place a coin far enough out that is completely clear of the table. On the other side, place a coin right up against the fold.
4. Grab the flap and give the cardboard a sharp, smooth twist. Your goal is to horizontally launch the coin that was placed up against the fold while allowing the other coin to drop straight to the ground. Listen for the sounds of the coins hitting the floor. What do you notice?

Results

Skateboard

You probably noticed that the ball went up and came right back down to the person on the skateboard, despite the fact that she was moving the whole time.

Coins

By listening to the coins, you will hear that they hit the floor at exactly the same time, even though one was shot out while the other dropped straight down.

Why?

Horizontal and vertical motion are completely independent of one another. If you stand in one spot and toss a ball straight up, it will come back to you. That’s probably not a surprise. But the ball also falls right back into your hands even if you are moving sideways the whole time. The vertical (up and down) motion of the ball knows absolutely nothing about the horizontal (sideways) motion. When you throw the ball up while riding the skateboard, the ball keeps going sideways. Because the ball retains its original horizontal motion after it leaves your hands, it ends up in your hands again as if neither you nor the ball had ever moved sideways in the first place.

The coin demonstration shows you the same thing, only a bit more dramatically. Both coins fall from the same height and begin falling at the same time. However, one is fired horizontally off the table while the other drops straight down. Intuitively, you might think that the launched coin should take longer to hit the ground because it has a greater distance to travel, but that’s not the case: they both hit the ground at the same time.  Remember: the coin’s vertical motion knows nothing about its horizontal motion, and gravity doesn’t care either way.  When figuring out how long it takes for either coin to hit the ground, all that matters is the height from which you’re dropping them.

Now you know enough to answer the original question: which bullet hits the ground first? The answer is they both hit the ground at the same time!