Since this is a quadratic equation, a plot of vertical position versus time should have the shape of a parabola. Notice that there are three variables here: position, time, and acceleration. If I know two of these, I can solve for the third. In this case, however, we only know the acceleration (g); we don’t have scales for distance or time.
So to nail down the distance, I estimated the width of Wonder Woman’s wrist at about 5 cm. Next, to circumvent the time problem, I created an arbitrary time unit, which I called fake seconds. Here then is a plot of vertical position versus time in fake seconds:
For the first part of this motion, the shape is parabolic, which means the bullet is indeed moving up with a constant downward acceleration. But check out that jump in the plot at around 2 (fake) seconds. That’s not right. Oh well. We can still do some fun stuff with this data. I’m just going to ask some questions and then go over the answers.
How long was the bullet in the air? What’s the real time scale?
Let’s assume my estimation of the distance scale was mostly legit. Mostly. That means I can find the vertical acceleration from the quadratic fit of the vertical bullet motion. This acceleration will be in units of meters per fake seconds squared instead of m/s2. But now, if I set this fake-time acceleration equal to the real acceleration, I can solve for the relationship between fake and real seconds:
