What Can You Do With This: Projectile Motion

Look carefully.

Download high quality here. See the pilot for instructions.

BTW: Lotta good stuff in the comments. I can’t prove any suggestion is better than another, but Jackie hits the one I intended all along, the one that packs the most punch per word, the one that rides into class alongside a student’s intuitive understanding of the world, the one that will do the most good as a introduction to parabolas:

Will the ball make it into the can?

Any question heavier than that and the picture starts to get a little wobbly under the weight.

BTW: Here are the still photos we imported into Geogebra and the full videos we used to confirm our answers.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Will the ball make it into the can? When is the height of the ball changing the fastest? The slowest? (although I think this picture would be easier to work with for those derivative questions). Graph the ball’s velocity vs. time. Estimate the horizontal distance the ball traveled. The vertical distance.

    Waiting to hear what others have to add to this.

    Nice work Dan!

  2. We’ve got constant vs. variable rates of change…which could lead into a discussion of what it really means when someone says a car ( or other object moving through space ) is traveling x miles per hour.

    We’ve got positive vs. negative slope and what that actually means in real space and time.

    Interesting photo.

  3. Copy the pic to SmartNotebook and give them a ruler with which to interact.
    If the thrower is 6’7″, what is the ball’s highest point?
    How far does the ball travel (horizontally)? When will the ball hit the ground?
    What was the initial (vertical) velocity of the ball?
    What was the initial horizontal velocity?
    Does the vertical velocity remain constant? Why?
    Does the horizontal velocity remain constant? Why?
    Describe how the slopes between the balls is changing? Will the slope ever equal zero? What does that mean?
    If we can determine the horizontal and vertical components, what was the actual velocity when the ball left the thrower’s hand?

  4. This is really nice, Dan.

    As Jackie said, Will the ball make it to the can? That’s a nice way to motivate fitting the data points to a parabola and extrapolate to the can.

    Another thing I really like is seeing how the balls get closer together as it flies. Is it reasonable for a teacher to point that out and wonder why? You don’t have to tell them about frame rate or the speed of the ball, but see if they come up with that?

    Do you have another version of this image with a grid superimposed?

    Perhaps you could try tweaking the contrast so the ball stands out more?

    Maybe another photo with the maestro running to catch the ball he’s thrown? You probably couldn’t superimpose yourself at 30 frames per second, but it would be funny nonetheless.

  5. Cool picture!

    I find myself wanting to reflect the path over a vertical line to see if it goes in, but it’s not obvious where the vertex is going to be. So I’m thinking we’d need a grid and a regression.

    If possible can you quickly describe how you made this?


  6. We did this today. A lot of fun. Basically, for all the good questions out here, only one of them is all that visceral, only one gloms onto the sticky part of a student’s brain. “Does the ball hit the can?”

    I have four variations on this theme. One that falls short, one that goes long, one that goes in, and one that looks like it goes in but illustrates the problem with 2D projections of a 3D space.

    We imported stills into Geogebra and modeled a parabola using sliders. Really effective.

    Kate, I filmed video using a little FlipCam and then exported a picture sequence from QuickTime. I imported all those frames into a Photoshop file and masked each frame down. Time consuming, but not hard.

  7. awesome shot. this is a lesson in a jpg.

    dan, is it easy to make sure that the stills you get from the movie are spaced out evenly by time?

  8. Andrew Ziobro

    March 24, 2009 - 6:03 pm -

    Great photo and idea. I was playing with you geogebra files and was wondering why you only fixed one corner of the photo.

    Did you discuss or attempt to scale the photo so that the equation was in “real” world units?

  9. I fixed one corner of the photo because I didn’t want my students to inadvertently move the photo around, nothing more than that. I’m pretty woefully bad with Geogebra, actually.

  10. Dan, is that a football field or a soccer field? On the photo, the horizontal line that your right foot is on appears to extend roughly 3/5 of the way to the trash can (where it makes a right angle with a line extending away from the camera) when it appears to end. Is that a penalty area on a soccer field? Also, are you a lefty or did you flip the photo?

  11. I shared this with my elementary students yesterday. They loved it and came up with great questions.

    My favorite was a student who wanted to know about the wind. He noticed the clouds in the background and said it looks like a storm brewing, that means the wind is coming. He also noted that a tennis ball is light and would be greatly effected by wind.

    I got an easy 20 minutes worth of great discussion out of this one picture. Keep them coming.

  12. How do you take the video and then flatten in so that the first 15 frames appear in one image? I can imagine doing this in photoshop, but it seems as though I’d have to export each frame and then merge them, which is rather time consuming.

  13. This is kind of an aside, but it might be interesting.

    I keep seeing this Bud Light commercial from the Super Bowl where a guy gets thrown out a window suddenly. The other day I noticed that he doesn’t fall parabolically. His chair falls away from him, but he appears to fall in a straight line, on some sort of cable I imagine.


    I just spent a little time trying to find this clip in a downloadable, editable manner but have come up short. If I could I would take a crack at editing some photos to illustrate it. At any rate, it’s another media source to illustrate what should be but isn’t parabolic motion. Maybe you can show it and then ask if they seen anything wrong with it, then show the actual path taken by the falling man/dummy and indicate how it really happened.

  14. tiredoldcliche

    March 31, 2009 - 10:04 am -

    Just thought i’d pop in to say i really enjoyed this one – used it with my kids in sunny England and they were well enthused. We went a step further and videoed them shooting free throws, and then trying to find the curve of their shot (similarly, working out if i’d used the shot they sank or the one they missed)

    One of those kids pointed me in the direction of vidshell (http://cripe03.rug.ac.be/Vidshell/Vidshell.htm) which enabled me to make photos like the one at the top in very little time at all – just upload the vid, and trace the path whilst it plays.

    Hope this reduces the time consuming aspect if you do anything like this again.

  15. Hi Dan,

    Wanted to let you know that I had a great Friday-before-spring-break lesson around this picture with a class that had just learned about modeling quadratics and creating equations from three points (both matrix-wise and using the calculator).

    I do have a SMARTBoard, so I had students up at the board marking up the picture, trying to figure out where to put coordinates, having me overlay a grid, and debating if real life scale matters (I noted how tall you are to give them a sense of scale for the photo and see if they used that or their own measuring stick). Didn’t have quite enough time to finish, but I’ll be splitting them up on Monday with the other pictures to have them tackle it again and share answers.

    Great day in math :) Thanks!

  16. Today in physics class, our teacher gave us our final exam project. We are in charge of teaching a certain chapter in our book. After looking at this a month ago, and seeing the option of “Projectile Motion”, I immediately took it. I’m using this in my presentation.

    This is some amazing stuff, I must say.

  17. Question – for every number on the set of 4 photos you have, is that 2 feet, a yard, or a meter?