3.1.1.P1

Prerequisite:

• Kinematic Graphs

In the reading, Kinematic Graphs, you saw a graph that tracked a ballet dancer's "grand jeté" motion. You may also have seen this in class or in a previous homework problem (Grand jete video) Here is the last frame of the video. Her eye was tracked frame by frame leaving little white dots as she performed her jump. The coordinate system we used is shown in yellow with the origin at the intersection of the x and y axes and the arrowheads indicating the positive direction for each variable.   We mentioned in that reading that the origin choice was arbitrary, and in fact, the orientation of the two perpendicular axes was also arbitrary. Let's see what we mean by that.

A. First, to remind yourself of what was done before, sketch 5 graphs: (1) the track of the x-y position of her eye as she jumped, (2) the x-position of her eye vs. time,  (3) the y-position of her eye vs. time, (4) the x-velocity of her eye vs. time, and (5) the y-velocity of her eye vs. time. On each of your graphs identify where her foot left the ground and where it touched the ground again. Explain why you drew the graphs the way you did.

B. Suppose we had chosen to put the origin of the axis at her eye in the first frame of the clip, orienting the axes the same way as shown above. Which graphs would change and how? Sketch them and explain your reasoning.

C. Suppose we had kept the origin where it was originally but chose the positive direction of x to be to the left (in the direction she was moving). Which of your graphs in A would change and how? Sketch them and explain your reasoning.

D. In general, explain what happens to the two velocity graphs if the origin is shifted to an arbitrary point and why you think it behaves as it does.

E. In general, explain what happens to the two velocity graphs if the direction of the x-axis, or the y-axis, or both are reversed and why you think it behaves as it does.

Alan Peel and Joe Redish 2/6/14