Mathspig noticed in the film that Katniss was aiming the arrow directly at the target. This is a problem. Arrows drop under gravity. If Katniss aims directly at the target she will hit it below her aim point. To overcome this she must raise her arrow aim.
What angle should she choose?
Robin Hood used a long bow and in the film Robin Hood archers raised their bows at a very high angle to cover long distances. See the diagrams below from Robin Hood Give Us Your Best Shot
According to The Flaming Arrow the speed of a modern arrow is 100 m/sec with a 65 lb draw weight.
Mathspig believes in using the SIMPLEST maths solution. In this case, very short arrow flight times are involved.
So we will assume the arrow velocity (Va) equals horizontal vector speed (Vx). This is an approximation that makes the maths sweet. Such an approximation might work for the arow flight in the first diagram (above), but not in the second.
First, mathspigs, we’ll calculate the arrow flight time to a target 100m away and then we will calculate the distance the arrow would drop vertically in that time as this will tell us the point in the air where Katniss should aim.
NB: An arrow will drop 4.9m over 100m to the target. In other words, Katniss would miss a human completely if she did not allow for gravity. Experienced archers automatically make this adjustment to their aim.