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/s^{2}. 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: