Calculating the largest arc, comes with background knowledge that the pieces being thrown away from the center point at a 45 degree angle will go the farthest (assuming no other external forces in this problem, as mentioned).
This means that the pieces from the firecracker, when it explodes 100m above ground, that are going in a 45 degree angle from that horizontal plane 100m above ground, will go the farthest horizontally. So we would be able to calculate the distance it goes horizontally by taking the horizontal component of the initial velocity, and plugging it into a formula to calculate the range of this projectile motion. (Note: At the point where it falls to the same plane; 100m above ground away from the original point... It moves even farther because of momentum and inertia while it's falling to the ground the rest of that 100m).
Aside from that, I am not too sure on how you would calculate the volume (all directions, not just left and right on a 2D representation,) for this explosion zone formed when it goes off. It would be more like a dome, so i'm sure there's some formula out there as well for this, which involves gravity, the displacement from the center, and the height).
But, there's also the area above that 45 degree blast arc, along with the point directly above the firecracker, and perpendicular to the ground.
