Teachers' Domain is moving soon to its new and improved home — PBS LearningMedia!          Learn More

# Predicting the Angle of a Bouncing Ball

Media Type:
Video

Running Time: 3m 05s
Size: 9.2 MB

or

Source: Cyberchase: "Penguin Tears"

### Collection Developed by:

Collection Credits

### Collection Funded by:

In this Cyberchase video segment, the CyberSquad is trapped in a cave. Inez and Digit have the key to escape, but there is an enormous block of ice in their way. In order to get the key to Jackie and Matt, who are on the other side of the cave, the CyberSquad decides to slide the key along the ice until it bounces off the cave wall and travels to the other side. Since they do not want to risk losing the key, they decide to use a small model. While testing the various aiming points, the CyberSquad learns about angles of reflection.

Background Essay

The Law of Reflection states that when an object hits a flat surface, the angle at which it approaches the surface will be equal to the angle at which it travels away from the surface. The angles are described as the angle of incidence (or the angle of entry) and the angle of reflection (or exit angle). An angle is made up of two rays with a common endpoint, called the vertex. The two rays that make up the angle of incidence are the ray along the object's path and the ray perpendicular to the surface, which is called the normal. The vertex of the angle is the point of impact (Note: this is not the angle to which Inez refers in the video. The angle she refers to as the "angle in" is the angle formed by the ray along the object's path and the ray formed by the wall).

It is important to mention that some particular conditions must exist in order for the Law of Reflection to be applied. The ball must be perfectly round, and not weighted in any part. And there can be no spin placed on the ball—that is, it cannot be spinning along an axis other than the horizontal one about which it moves toward the wall. The surface that the ball hits must be completely flat and not able to be moved upon impact. Also, there can be no other external force applied to the ball, as that may change its direction. For example, if a person pushes the ball or a wind gust affects it or the ball hits some bumps on the surface, then its path will change. If any of the conditions are not met, the Law of Reflection cannot be applied to the situation.

The Law of Reflection may come in handy when playing a game of pool, but the proper conditions must be met (i.e. smooth surfaces on the pool table and no spin on the ball). The Law of Reflection is also applied to the path light takes when it is reflected off a mirror. The light reflection angle will equal the measure of its angle of incidence. A periscope makes use of this property in allowing a person to see an object that is not in their direct line of sight. A periscope works by using two mirrors positioned parallel to each other and at a 45° angle to the object and the viewer's eye. The light from the object reaches one mirror, bounces to the other, and then reaches the viewer's eye.

Discussion Questions

• What does the CyberSquad learn about the angle-in and angle-out when an object bounces off a wall?
• Can you think of any other sports or activities in which this idea could be useful?
• How does creating a model help the CyberSquad find a solution?
• What do you think might happen if the flat surface hit by the ball moves? What if the ball is not weighted evenly? Can you think of some experiments you could conduct to answer these questions?

Transcript

INEZ: There’s no way to get the key over there!

MATT: No problem. We’ll just wait here till this whole place melts!

JACKIE: Matt, this is no time for jokes! Inez, you’ve gotta get it here somehow, or we’ll never get out!

DIGIT: Too bad Ice isn’t here. She could bounce the key off the back wall right into Matty’s mitts! Slap shot, baby!

MATT: But the ice in front of us is full of holes. You’ll have to make exactly the right shot - or the key will fall into a hole. Then what?

JACKIE: But how do we do that? We can’t even see each other! And besides, there’s no aiming point!

INEZ: Aiming point! What’s that got to do with anything?

MATT: I’m not sure - but I know that’s how Ice makes all her shots work.

JACKIE: Yeah! Inez, whenever Ice stands in a certain spot and aims for a certain spot on the wall, her shots always go where she wants.

FLUFF: There’s no way we can figure that out!

DIGIT: Maybe we can. Our own little practice rink!

INEZ: Cool! Let’s use it to try out some shots and figure out why aiming spots work.

FLUFF: Would one of these candies help? They’re flat and round like the key.

INEZ: Great idea Fluff, thanks.

MATT: Hey, guys! We can’t see what you’re doing. What’s going on?!

DIGIT: Check your skwak for a Bird’s Eye View!

JACKIE: Thanks, Didge. We see it!

INEZ: Okay, this spot marks where we are...and this spot is where you guys are...and here’s the iceberg between us.

MATT: Got it!

INEZ: I’m gonna try and bounce this candy off the back of the drawer over to you spot.

INEZ: I missed! My aiming spot is too far to the right!

JACKIE: Try another aiming spot, Inez.

INEZ: Oh! Missed again. Now my spot’s too far to the left!

MATT: C’mon, Inez, you can do it!

INEZ: Think I’ve got it aimed right this time.

DIGIT: And we’ve got a winner! Whoo hoo!

FLUFF: But how’s this gonna help us know where to aim?

FLUFF: Three different shots, three different paths, only one winner. So what!

INEZ: Different paths, but look, something is the same for each one. Check out the angles the paths make with the wall.

DIGIT: Angles!!! Now what are you talking about, Nezzie?

INEZ: Just look at this shot Didge. See where I hit the wall with the candy? I’m talking about the angle right here, between the path going in and the wall.

DIGIT/FLUFF: Uh - huh...

INEZ: Now look at this angle over here. Here’s the angle of the candy coming out from the wall. Notice anything?

DIGIT: They look like they’re the same.

INEZ: I think that’s the secret to making a perfect shot.

DIGIT: The angle that the path makes going into the wall is the same as the angle the path makes coming away from the wall. Who knew?!

MATT: I bet it’s a rule that works for all bounces. The angle in is the same as the angle out.

Standards

to: