The primary task of the attacker artillery was to knock out the defender artillery andsuppress the defenders at the parapet (top of the horizontal hill) see diagram. What are the minimal and maximal horizontal ranges of the attacker artillery, firing from the outer perimeter and trying to hit the parapet? parapetH=15m70°moata=30mescarpmentouter perimeter|h=6m Setup. A historical Vauban bastion fortification features a horizontal-top hill of heightH=15 meters. Viewed in a vertical cross-section perpendicular to its face, the hill slopesdown from the parapet at 70 degrees from the horizontal, towards a horizontal moat oflength a=30 meters, which terminates at an escarpment of height h=6 meters above themoat. The outer perimeter starts from the top of the escarpment and continues outwardhorizontally. The inspiration example is the Jaca citadel in Spain (see aerial photo below).A diagram of the setup is provided below.A group of young modern enthusiasts is using the historical fortification for recreation.Their gas cannons hurl small pumpkins at 30 m/s initial velocity. These cannons can beelevated up to 30 degrees and depressed down to -10 degrees. The defending artillery isstationed at the parapet of the bastion, i.e. at the top edge of the hill. You can ignore airresistance. Assume all firing is done perpendicular to the face of the bastion (i.e. in theplane of the diagram below).

Name: The primary task of the attacker artillery was to knock out the defend
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Description: The primary task of the attacker artillery was to knock out the defender artillery andsuppress the defenders at the parapet (top of the horizontal hill) see diagram. What are the minimal and maximal horizontal ranges of the attacker artillery, firing

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The primary task of the attacker artillery was to knock out the defender artillery and suppress the defenders at the parapet (top of the horizontal hill) see diagram. What are the minimal and maximal horizontal ranges of the attacker artillery, firing from the outer perimeter and trying to hit the parapet?

parapet
H=15m
70°
moat
a=30m
escarpment
outer perimeter
|h=6m

Setup. A historical Vauban bastion fortification features a horizontal-top hill of height
H=15 meters. Viewed in a vertical cross-section perpendicular to its face, the hill slopes
down from the parapet at 70 degrees from the horizontal, towards a horizontal moat of
length a=30 meters, which terminates at an escarpment of height h=6 meters above the
moat. The outer perimeter starts from the top of the escarpment and continues outward
horizontally. The inspiration example is the Jaca citadel in Spain (see aerial photo below).
A diagram of the setup is provided below.
A group of young modern enthusiasts is using the historical fortification for recreation.
Their gas cannons hurl small pumpkins at 30 m/s initial velocity. These cannons can be
elevated up to 30 degrees and depressed down to -10 degrees. The defending artillery is
stationed at the parapet of the bastion, i.e. at the top edge of the hill. You can ignore air
resistance. Assume all firing is done perpendicular to the face of the bastion (i.e. in the
plane of the diagram below).

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These solutions are the solutions for the defender artillery from the parapet. The question is asking for the minimal and maximal ranges of the attacker artillery from the outer perimeter to the parapet. Are the minimal and maximal ranges the same for both?

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