Catching speeders from our math class
Instead of using a worksheet, or pseudo-context question from a textbook you can show how related rates can be used to estimate the speed of a car from our classroom window.
1) I used the Distmeasure app to determine the distance my classroom window is from the road.
2) A student extended his arm and followed a car with arm until it hit a 45 degree angle. Different students timed how long it took and we averaged the times. [This will allow us to calculate the average rate of change of his arm in radians/second] in our class this took 4.6 seconds, as the following:
3) Perform the calculations below
Since we know that student stopped at 45 degrees we can use the special triangle of 45/45/90 to substitute into the above formula.
4) Talk about the limitations of this activity, and how accurate this is.