## Thursday, February 25, 2010

### Vertical Motion

One of my favorite things to do with quadratics is work with the vertical motion model. The way I introduce this is to show something like this video:

or this one:

Note: I have downloaded the video files for offline use as YouTube is blocked in my district. I have also edited these videos so students do not know what the starting heights are.

A pretty good discussion usually ensues about how a falling object is accelerating as it approaches the ground. I'll ask students what information would they find interesting. Responses usually include but are not limited to:

1. How high was he when he jumped?
2. How fast was he going when he hit the water?
3. How long was he in the air?

The easiest to answer is "How long was he in the air?" simply because we can set a stop watch to the problem and figure it out.

From there we can use the vertical motion model to find out how crazy one must be to earn a world record high dive.

I find the toughest thing about teaching vertical motion is the fact that my students have a tough time recognizing the resulting parabola is not the actual path of the ball, but the graph of height vs. time.

I have found this applet to be an invaluable resource in teaching vertical motion.

I have been thinking for a while about adding a problem which includes a horizontal velocity to this unit, but really had no way to do it. Last year I threw this post of Dan's in front of my kids and they came up with this. The tough part about working with the horizontal velocity component is helping students realize that vertical and horizontal forces don't have an effect on each other. The best sources I have found in helping explain this concept are this (h/t Rhett Allain) and this.

However, recently I enlisted the help of Dr. Linda Fahlberg-Stojanovska to create a GeoGebra applet that would model a problem that involves vertical motion with horizontal velocity.

I really like this applet because of the iterative feature. I love that I now know how to get rid of the sliders so as to eliminate the cheat factor.

Student Response:
They LOVE the applets. When they can actually see that their calculations work out, they get pretty excited. I've had some students become interested in making their own which may turn into a pretty cool project.

For the kids who still have trouble understanding the independence between the horizontal and vertical components of this problem, I tried to appeal to their ELA sensibilities regarding point of view.

Tell the story from the vertical point of view.

Object is dropped from 's' starting height and falls for 't' seconds before hitting the ground.

Equation used: $y = -16t^{2}+s$

Tell the story from the horizontal point of view.

Object travels at 'r' miles per hour for 't' seconds before hitting the ground.

Equation used: D = rt