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).
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).
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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What is the width of the kill zone, i.e. the zone where the attackers would be vulnerable
to defender fire?
Transcribed Image Text:parapet
H=15m
70°
moat
a=30m
escarpment
outer perimeter
|h=6m
Transcribed Image Text: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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Step 1: Determine the given data:
VIEWStep 2: Calculate the OC distance:
VIEWStep 3: Determine the height of the projectile when projected with angle theta 2 when it travels OC:
VIEWStep 4: Determine the height of the projectile when projected with angle theta 1 when it travels OC:
VIEWStep 5: Determine the Horizontal distance traveled by projectile when projected at theta 1:
VIEWStep 6: Calculate the width of the kill zone:
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