Let the firecracker start at point (0,0) in the figure. The position of the fragments after the explosion, in the absence of the ceiling and the floor, is described by the equations:
Combining these equations, we can obtain the expression of the parabolic motion:
Now the effect of the ceiling needs to be considered. The collisions of the fragments with the ceiling are elastic, and their vertical speed would be reversed upon the impact, thus reducing the attained range. The challenge is to find the angle α for which the trajectory is tangent to the ceiling, allowing the fragments just barely graze...
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