## Tuesday, June 23, 2015

### Trajectories of an Arrow

In archery and shooting sports, a tiny difference of aim can result in a big difference at the target. Consider the trajectories of two arrows below, both excerpted from The Science of Archery & Shooting Sports: Volume 1 from Schottenbauer Publishing.

Discussion Questions
1. Which graph shows an arrow moving in a straight line?
2. Which graph shows an arrow moving up and down?
3. Why are points missing in the second graph? Sketch in the trajectory which is most likely during this segment of time.
4. Redraw each graph using a similar scale on each axis.
5. Redraw each graph using a similar scale on each axis, and re-labeling the origin of the tip of the arrow at x=0, y=0, and t=0.
6. Draw the motion of each arrow on a separate piece of paper, using the information from #5 above.
7. On the drawings from #6 above, add labels showing time at (a) release from the bow, (b) apex, (c) final point.
8. Describe the range of x, y, and t for each graph, using the information from #5.
9. Which arrow travels further in the x direction? In the y direction?
10. Describe the absolute distance which each arrow travels. Which arrow travels further, in absolute distance?
11. Which arrow is in flight for a longer period of time?
12. For each graph, draw the arrow in starting position. Using a compass, measure the angle.
13. Which arrow was aimed better? What information is necessary to answer this question?

Graphs and data on archery and shooting sports can be found in the following science lab manuals from Schottenbauer Publishing:

Anthologies of 28 Graphs