In lecture, I often held a piece of chalk to my nose and let it fall to the floor. It lands
between my feet. (a) Draw a careful sketch of the trajectory in a space-time diagram
as you record it. (b) Estimate using dimensional arguments how long it took to fall.
Is this result consistent with your experience from dropping things? Describe a simple
experiment, fairly precise, that you could perform right now to check this time. Don’t
do it just describe it. (c) Draw the trajectory as I record it. (d) Redraw your sketches
in parts (a) and (c), and on both sketches for the time halfway through the fall, show
where the chalk is and where my feet and my nose are.
I have also often gotten on a skateboard held the chalk to my nose and released it.
(e) Draw a careful sketch of this trajectory as I record it. (f) How long do I think
it took to fall? (g) Draw the trajectory of my feet and my nose on your space-time
diagram. Start with your feet coincident with my feet at the time of release. (Hint:
you may need more than one spatial dimension.) (h) Redraw your sketch in part (g)
and carefully sketch the trajectory of the chalk as you record it. (i) Again redraw your
sketches in parts (e) and (h), and on both sketches for the time halfway through the
fall, show where the chalk is and where my feet and my nose are. (j) Redraw your
sketch in part (e) adding the trajectory of your feet on my space-time diagram and the
one for the chalk. (k) Of all these sketches in the problem what ones look essentially
the same? What are the implications of this result? (l) Let say that we want to discuss
chalk moving naturally from nose to feet but in half the time. Sketch this in my frame for both the case with and without the skateboard. (m) I now want the time of fall to
be double the simple release at the start of this discussion. Sketch those trajectories.