## Real-life Linear Relationships: Racing Cars + Flying

I was scanning through the internet a few days ago when I noticed a blog called mathsclass written by Simon Job. It’s a great blog with some brilliant ideas, one of which I used with my year 8 class to solidify the concept of real-life linear relationships.

I asked my students to bring in a toy car (with a pull-back mechanism) and said that we were going to do some racing in the next lesson. When the next lesson came we had more than enough cars for everyone so we went to the hall to collect some results. We put tape measures down in the hall and measured the pull-back distance as the input and the distance travelled as the output. At the end, we had a race and then went back to class to graph the results.

Firstly, it was beneficial for the students to see that real life linear relationships exist and they are usually not exactly linear. Indeed, some of the cars had problems with veering to the left or right when the pull-back distance increased. We also found that many of the cars had a ´critical distance´ that they could not surpass – no matter how big the pull-back distance was. This is of course down to the fact that the wind-back mechanism has a limit so you are essentially pulling the car back with no further increase in wind-back. This led into an interesting discussion on restricting the function/breaking up the function into two parts. (nice intro to piece-wise functions!)

An awesome idea, both in terms of how much fun we had and how much we learnt.

Thanks Simon!

Update: 23rd March 2013

The new Emirates planes provide excellent info on the flight details such as the bearing of the plane, the altitude, air temperature, speed, etc. On the descent into Dubai, I recorded the air temperature at different altitudes. It came as little surprise that the relationship is linear.

Having said this, if you go beyond the normal altitude of commercial aircraft, the relationship becomes more interesting.

http://www.ux1.eiu.edu/~cfjps/1400/atmos_struct.html

(Figure 1-19, p. 20 in Lutgens and Tarbuck’s The Atmosphere, 2001)
Thermal structure of the atmosphere