# Activity Guide: Projectile Motion

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Jugglers know that if you throw a ball, a bean bag, or a pin into the air, it will follow a curved path. This curve is what naturally happens when an object can move in two dimensions—horizontal and vertical—at the same time. As the ball moves horizontally, gravity pulls down. Physicists call this projectile motion. This unit helps students understand why any projectile, no matter if thrown, shot, or launched, will follow a curved path while in the air.

## How to Incorporate the Video Into Instruction

This video can be used to motivate the study of projectile motion, velocity, acceleration, and the broader case of two-dimensional motion. It can also serve as an extra illustration to reinforce previous lessons on these topics.

### Questions to Ask Students Before Watching the Video

- What determines how high a juggling pin goes?
- What determines how far it travels horizontally while in the air?
- How does the change in the pin’s vertical velocity compare to the change in horizontal velocity?

## Watch the Video

## Circus Physics: Projectile Motion

In this video students will learn why any projectile, no matter if thrown, shot, or launched, will follow a curved path while in the air.

### Questions to Kick-Start Class Discussion After viewing the Video

- What determines how many objects a person can juggle?

It’s a combination of the time each pin stays in the air and the max height a person can throw something. If time and space allow, you could ask students to throw a tennis ball as high as they can and time it to see what the range of air times are. - As you throw a ball higher, why is it harder to have it come back down in the same place?

Small horizontal velocity over the time of flight means the object can have significant drift. - Does the spinning of the juggler’s pin affect how long it’s in the air?

No, though the spin makes for a more stable path, negating some of the affects of air-resistance. - How does air resistance change things?

It reduces both horizontal and vertical velocities. - Would juggling be the same on the Moon? How about Jupiter?

Gravity is weaker on the Moon, so a juggler could throw pins higher and could conceivably juggle more pins than on Earth, but with such long hang-times, horizontal drift could make this difficult. Jupiter’s gravity is much stronger, so hang time would be less, which implies a juggler would not be able to juggle as many pins as on Earth.

Most sports use a projectile of some sort: basketball, baseball, soccer, football, tennis, ping-pong. Some sports, like long jump, high jump, and snowboard half-pipe turn the human body into a projectile.

## Suggested Classroom Activities

### Activity 1: Juggling in Space

Have students use the height equation to plot a ball’s height vs. time on three different planets: Earth, the Moon, and Jupiter. The acceleration due to gravity on Earth is 9.8 m/s², the Moon: 1.6 m/s², Jupiter: 26 m/s².

First, have students “juggle” one ball, timing how long it takes to come back down to their hand. By dividing this number by two, they can find the time it takes to reach the max height. From there they can calculate what the initial velocity was by re-arranging the max-height equation. Students can then chose appropriate time increments to plot the trajectory.

H_{max} = V_{initial} x time + (½) x gravity x time²

Ask them to estimate the max height from their plots. If time, ask how they could find the max height exactly.

If students have access to the Internet, after they have plotted each trajectory, they can check that their answers make sense by comparing with the paths plotted by an online projectile applet, such as the one found at: http://www.walter-fendt.de/ph14e/projectile.htm

### Activity 2: The Giant Parabola

Construct, or have students construct, a giant parabola in the classroom, using butcher paper and markers or paint. Any easy way to do this is to first mark all of the square numbers on a meter stick (1, 4, 9, 16, etc.). Move the meter stick in regular increments, marking each of the squares for the vertical coordinate in turn. Connecting these points with a smooth curve should produce a nice big parabola.

Once the parabola is made, hang it in the classroom. Ask students to stand at one end and throw objects along the curve and observe how closely their paths conform to the parabola.

If you have space, such as a large gymnasium, one idea is to have students construct a parabola by tying together a chain of helium filled balloons. If you have access to a video camera, you can record students throwing objects, then go back and watch how closely they follow the path in slow motion.

### Activity 3: Projectile Motion Video Analysis

To do this activity you will need to download the video "Video Analysis: Projectile Motion." You can use VideoPoint or similar software for graphing and analysis.

The Circus series is full of examples of projectile motion, from the trapeze artists flying through the air, to the jugglers passing clubs, and in Anna’s performance on the Russian Barre.

In each you should have students mark the position of the object and then make a graph of the vertical position. A screen capture from a video software analysis of Anna is produced below:

As you might notice right away there is a small deviation from a perfect parabola. When selecting a video it is important to find a clip where the camera is not panning. Still, using the data one gets a rather perfect parabolic motion, and LoggerPro allows for curve fitting. By selecting the height of the performers to be around two meters, the program yields the acceleration of gravity to be around 9.4 m/s/s.

Have students try this with the other videos provided.