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Battleships! In 1905, as part of the Russo-Japanese War, the Imperial Japanese Navy (IJN) under the command of Admiral Togo engaged the Russian fleet under the command of Admiral Rozhestvensky in the Battle of Tsushima. This was the first major naval engagement to be dominated by "big guns." In this question we will model the 12" Armstrong Whitworth guns employed by the IJN. The guns are capable of firing a 390kg shell at a speed of 732ms-1. For simplicity, we shall assume that this shell is a sphere of diameter D such that the drag due to air resistance can be approximated as Fp 2 CppAv² 16PDu² = cv? where Cp= 1/2 is the approximate drag coefficient for a sphere, A = T(D/2)2 is the reference area, p ~ 1.225kgm-3 is the density of air at sea level, and v is the velocity, whence C = 16PD? The overall force experienced by our shell in flight is hence F = mg - cv²v , where m is the mass of the shell and g is the acceleration due to gravity, v= and v^ = v/v, with v corresponding to the velocity vector. We shall take our coordinate system such that x^ points east, y^ points north, and z^ points up whence g-9.81z^. With this, let our gun be placed at the origin of our coordinate system, and assume our ship is at rest. We shall model the ship we are trying to hit with our shell as having a length of 121m, a beam of 23m, and being purely rectangular in shape. At t = 0 let the midpoint of this ship be located 4km to the north and 6km to the east of us, steaming with a speed of 7.5ms-1 in a south-southeast direction.

Battleships! In 1905, as part of the Russo-Japanese War, the Imperial Japanese Navy (IJN) under the command of Admiral Togo engaged the Russian fleet under the command of Admiral Rozhestvensky in the Battle of Tsushima. This was the first major naval engagement to be dominated by "big guns." In this question we will model the 12" Armstrong Whitworth guns employed by the IJN. The guns are capable of firing a 390kg shell at a speed of 732ms-1. For simplicity, we shall assume that this shell is a sphere of diameter D such that the drag due to air resistance can be approximated as Fp 2 CppAv² 16PDu² = cv? where Cp= 1/2 is the approximate drag coefficient for a sphere, A = T(D/2)2 is the reference area, p ~ 1.225kgm-3 is the density of air at sea level, and v is the velocity, whence C = 16PD? The overall force experienced by our shell in flight is hence F = mg - cv²v , where m is the mass of the shell and g is the acceleration due to gravity, v= and v^ = v/v, with v corresponding to the velocity vector. We shall take our coordinate system such that x^ points east, y^ points north, and z^ points up whence g-9.81z^. With this, let our gun be placed at the origin of our coordinate system, and assume our ship is at rest. We shall model the ship we are trying to hit with our shell as having a length of 121m, a beam of 23m, and being purely rectangular in shape. At t = 0 let the midpoint of this ship be located 4km to the north and 6km to the east of us, steaming with a speed of 7.5ms-1 in a south-southeast direction.

Elements Of Electromagnetics
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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Battleships! In 1905, as part of the Russo-Japanese War, the Imperial Japanese Navy (IJN) under the command of Admiral Togo engaged the Russian fleet under the command of Admiral Rozhestvensky in the Battle of Tsushima. This was the first major naval engagement to be dominated by "big guns." In this question we will model the 12" Armstrong Whitworth guns employed by the IJN. The guns are capable of firing a 390kg shell at a speed of 732ms-1. For simplicity, we shall assume that this shell is a sphere of diameter D such that the drag due to air resistance can be approximated as 1 FD CopAv² where Cp = 1/2 is the approximate drag coefficient for a sphere, A = T(D/2)2 is the reference area, p - 1.225kgm-3 is the density of air at sea level, and v is the velocity, whence C = 16 pD? The overall force experienced by our shell in flight is hence F = mg – cvv , where m is the mass of the shell and g is the acceleration due to gravity, v= v and v^ = v/v, with v corresponding to the velocity vector. We shall take our coordinate system such that x^ points east, y points north, and z^ points up whence g--9.81z^. With this, let our gun be placed at the origin of our coordinate system, and assume our ship is at rest. We shall model the ship we are trying to hit with our shell as having a length of 121m, a beam of 23m, and being purely rectangular in shape. At t = 0let the midpoint of this ship be located 4km to the north and 6km to the east of us, steaming with a speed of 7.5ms-1 in a south-southeast direction.
Transcribed Image Text:Battleships! In 1905, as part of the Russo-Japanese War, the Imperial Japanese Navy (IJN) under the command of Admiral Togo engaged the Russian fleet under the command of Admiral Rozhestvensky in the Battle of Tsushima. This was the first major naval engagement to be dominated by "big guns." In this question we will model the 12" Armstrong Whitworth guns employed by the IJN. The guns are capable of firing a 390kg shell at a speed of 732ms-1. For simplicity, we shall assume that this shell is a sphere of diameter D such that the drag due to air resistance can be approximated as 1 FD CopAv² where Cp = 1/2 is the approximate drag coefficient for a sphere, A = T(D/2)2 is the reference area, p - 1.225kgm-3 is the density of air at sea level, and v is the velocity, whence C = 16 pD? The overall force experienced by our shell in flight is hence F = mg – cvv , where m is the mass of the shell and g is the acceleration due to gravity, v= v and v^ = v/v, with v corresponding to the velocity vector. We shall take our coordinate system such that x^ points east, y points north, and z^ points up whence g--9.81z^. With this, let our gun be placed at the origin of our coordinate system, and assume our ship is at rest. We shall model the ship we are trying to hit with our shell as having a length of 121m, a beam of 23m, and being purely rectangular in shape. At t = 0let the midpoint of this ship be located 4km to the north and 6km to the east of us, steaming with a speed of 7.5ms-1 in a south-southeast direction.
d? xx C C -9.81-–viz î VXX vyy m m m (c) Assuming our gun is directed with an azimuthal angle p to thex-axis and an elevation of 0 such that it makes a polar angle of T/2 – 0 with the z-axis, state the six initial conditions for our system of ODES. Hint: Recall that our gun is positioned at the origin and that our shells have an initial velocity of 732ms-1, (d) Given values of 0 and p we may begin to numerically solve our system of ODES. State the termination condition for our simulation; that is to say at what time t should we stop running our solver?
Transcribed Image Text:d? xx C C -9.81-–viz î VXX vyy m m m (c) Assuming our gun is directed with an azimuthal angle p to thex-axis and an elevation of 0 such that it makes a polar angle of T/2 – 0 with the z-axis, state the six initial conditions for our system of ODES. Hint: Recall that our gun is positioned at the origin and that our shells have an initial velocity of 732ms-1, (d) Given values of 0 and p we may begin to numerically solve our system of ODES. State the termination condition for our simulation; that is to say at what time t should we stop running our solver?
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