Sweden and Norway are at war over who makes the best pickled herring. You are in charge of a Swedish artillery unit that is trying to shoot at some Norwegians located 1000 meters away at the same height as you are. If we neglect the friction of the air, the cannon ball follows a parabolic trajectory; as you certainly recall from prior courses, a cannon ball travels a distance L = V² sin(2a) 9 where Vis the initial velocity, a is the angle of the cannon barrel, and g = 9.8 m/s² is the gravitational acceleration. You realize that you only have two options for how to shoot. Option (1) is to use 1 bag of gun powder, which produces an initial velocity of exactly V₁ = 105 m/s, and to try to set the angle to αI,nominal = 39 degree. Option (II) is to use 2 bags of gun powder, which produces exactly V₁ = 137 m/s, and to try to set the angle to αII,nominal = 15 degree. If you set the angles exactly to the nominal ones, compute the traveling distances. L₁ = LII = number (rtol=0.05, atol-0.0001) number (rtol=0.05, atol-0.0001) ? ?

Sweden and Norway are at war over who makes the best pickled herring. You are in charge of a Swedish artillery unit that is trying to shoot at some Norwegians located 1000 meters away at the same height as you are. If we neglect the friction of the air, the cannon ball follows a parabolic trajectory; as you certainly recall from prior courses, a cannon ball travels a distance L = V² sin(2a) 9 where Vis the initial velocity, a is the angle of the cannon barrel, and g = 9.8 m/s² is the gravitational acceleration. You realize that you only have two options for how to shoot. Option (1) is to use 1 bag of gun powder, which produces an initial velocity of exactly V₁ = 105 m/s, and to try to set the angle to αI,nominal = 39 degree. Option (II) is to use 2 bags of gun powder, which produces exactly V₁ = 137 m/s, and to try to set the angle to αII,nominal = 15 degree. If you set the angles exactly to the nominal ones, compute the traveling distances. L₁ = LII = number (rtol=0.05, atol-0.0001) number (rtol=0.05, atol-0.0001) ? ?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.

Question

Sweden and Norway are at war over who makes the best pickled
herring. You are in charge of a Swedish artillery unit that is trying
to shoot at some Norwegians located 1000 meters away at the
same height as you are. If we neglect the friction of the air, the
cannon ball follows a parabolic trajectory; as you certainly recall
from prior courses, a cannon ball travels a distance
L =
V²sin(2a)
9
where V is the initial velocity, a is the angle of the cannon
barrel, and g = 9.8 m/s² is the gravitational acceleration.
You realize that you only have two options for how to shoot.
Option (I) is to use 1 bag of gun powder, which produces an
initial velocity of exactly V₁ = 105 m/s, and to try to set the
angle to aI,nominal = 39 degree. Option (II) is to use 2 bags of
gun powder, which produces exactly VII = 137 m/s, and to try
to set the angle to aII,nominal = 15 degree.
If you set the angles exactly to the nominal ones, compute the
traveling distances.
L₁ =
LII
=
The problem is that the cannon is old with a rusty mechanism -
you can't set the angle to exactly the value you want. You can
model the actual angle as a random variable that is normally
distributed around nominal with a nominal standard deviation of 1
degree. Under this scenario, which option is the best? Use the
approximate formulas for the mean and standard deviation of a
nonlinear function of a random variable (the "error-propagation
formula").
σI =
number (rtol=0.05, atol=0.0001)
number (rtol=0.05, atol=0.0001)
σII =
number (rtol=0.05, atol=0.0001)
number (rtol=0.05, atol=0.0001)

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