Artillery A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point ( x , y ) at time t according to the relationship cot θ = 2 x 2 y + g t 2 where θ = the angle of elevation of the launcher and g = the acceleration due to gravity = 32.2 f e e t / s e c o n d 2 . An artilleryman is firing at an enemy bunker located 2450 feet up the side of a hill that is 6175 feet away. He fires a round, and exactly 2.27 seconds later he scores a direct hit. (a) What angle of elevation did he use? (b) If the angle of elevation is also given by sec θ = v 0 t x , where v 0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
Artillery A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point ( x , y ) at time t according to the relationship cot θ = 2 x 2 y + g t 2 where θ = the angle of elevation of the launcher and g = the acceleration due to gravity = 32.2 f e e t / s e c o n d 2 . An artilleryman is firing at an enemy bunker located 2450 feet up the side of a hill that is 6175 feet away. He fires a round, and exactly 2.27 seconds later he scores a direct hit. (a) What angle of elevation did he use? (b) If the angle of elevation is also given by sec θ = v 0 t x , where v 0 is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
Artillery A projectile fired into the first quadrant from the origin of a coordinate system will pass through the point
at time
according to the relationship
where
the angle of elevation of the launcher and
the acceleration due to gravity
. An artilleryman is firing at an enemy bunker located 2450 feet up the side of a hill that is 6175 feet away. He fires a round, and exactly
seconds later he scores a direct hit.
(a) What angle of elevation did he use?
(b) If the angle of elevation is also given by
, where
is the muzzle velocity of the weapon, find the muzzle velocity of the artillery piece he used.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
8d6 عدد انباء
Q/ Design a rectangular foo
A
ing of B-2.75m to support a column of
dimensions (0.46 x 0.46) m, dead load =1300kN, live load = 1300kN,
qa-210kPa, fc' 21 MPa, fy- 400 MPa.
=
Q1/ Two plate load tests were conducted in a C-0 soil as given belo
Determine the required size of a footing to carry a load of 1250 kN for the
same settlement of 30 mm.
Size of plates (m) Load (KN) Settlement (mm)
0.3 x 0.3
40
30
0.6 x 0.6
100
30
Qx 0.6z
The OU process studied in the previous problem is a common model for interest rates.
Another common model is the CIR model, which solves the SDE:
dX₁ = (a = X₁) dt + σ √X+dWt,
-
under the condition Xoxo. We cannot solve this SDE explicitly.
=
(a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler
scheme to simulate a trajectory of the CIR process. On a graph, represent both the
trajectory of the OU process and the trajectory of the CIR process for the same
Brownian path.
(b) Repeat the simulation of the CIR process above M times (M large), for a large
value of T, and use the result to estimate the long-term expectation and variance
of the CIR process. How do they compare to the ones of the OU process?
Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000.
1
(c) If you use larger values than above for the parameters, such as the ones in Problem
1, you may encounter errors when implementing the Euler scheme for CIR. Explain
why.
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