Zach's Experiment

In order for Zach to discover whether or not the crows had a good reason to fly to this average height of 5.6 m to drop the whelks, he conducted his own whelk-dropping experiment. He dropped 12 large whelks from each height of 2, 3, 4, 5, 6, 7, 8, 10, and 15 metres. He then calculated the average number of drops it took for the whelks to break from each of these heights.

Exercise 1: What do you think the graph of average number of drops as a function of height will look like? Sketch your idea on a grid, with height on the x-axis and average number of drops before breakage on the y-axis. What type of curve did you draw, and why?

Exercise 2: Answer the following questions:

a) Does the curve you sketched in Exercise 1 match the shape of the curve formed by the data above? If not, does the figure above make sense to you? Explain why a large number of drops is required for a small height, and a small number of drops for a large height.

b) Suppose that a particular crow always flies up to a height of 4 metres to drop the whelk. Can you say how many times the crow will need to drop the whelk before it breaks? Is there a minimum or maximum number of drops it could take? What is the meaning of average number of drops?

c) Do you think it makes sense for a crow to fly up to a height of 20 metres? Why or why not?

d) Do you think it makes sense for a crow to fly up to a height of 2 metres? Why or why not?

e) Why do you think the crows consistently fly up to a height of around 5 or 6 metres?