The three multiple choice options my physics teacher gave for this example problem

That's technically wrong. I'll repost my comment from elsewhere.

That's only if the bullet was travelling sufficiently fast. Essentially, your plate had some wiggle room, so if you aimed at the middle, you would clip the top.

x=A * t2 + V_0 * t + x_0. Right?

So in the case of the plate you have:

x= (9.8) * t2 + plateheight

And in the case of the bullet you have

x= (9.8) * t2 + V_0 * t

These are only exactly the same when V_0 * t = plate height. But in reality, plate height is, say, 2 meters +- .2 meters because it is not a point but an object with dimensions, so you have some wiggle room. The objects collide after t=V_horizontal / distance between plate and gun. As long as the difference between V_vertical * t and plate height is less than the radius of the plate, the objects will collide. This was why they always hit in your class. Because t is very small, and V_vertical times t is very small and always less than the radius of the plate. If the bullet is fired from the same height as the falling object, than V_0 is 0 and plate_height and gun_height are the same so x is the same for both. But if they are not fired with the same position and starting velocity x will not be the same.

/r/CrappyDesign Thread Parent Link - i.imgur.com