6) a)Define a coordinate system on the Earth at a colatitude of θ such that z...

6) a)Define a coordinate system on the Earth at a colatitude of θ such that z is pointed radially outward along the radius of Earth, y is pointed to the North, and x is pointed to the East. Using the fact that the Earth rotates as some constant angular velocity ω pointed“up” along the axis of rotation, derive the general expression for the x, y, and z accelerations for an object thrown with some initial velocity [ v0=(v0 x , v0 y , v0 z ) ] just above the surface of the Earth. This object moves under the influence of gravity and the Coriolis Force. [Hint: Use zeroth order approximation of acceleration with respect to ω and the initial condition to substitute for the velocity terms]

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genius_generous answered 2 years ago

3. Suppose we have a coordinate system (x, y, z) with the origin at one corner...

3. Suppose we have a coordinate system (x, y, z) with the origin at one corner of a cube, and the axes parallel to the edges of the cube. We want to perform a rotation to a coordinate system (x' , y' , z' ), where the x 0 axis is along the diagonal of the cube, and the y' axis remains in the original x ? y plane. (a) (0.5 points) Using the Z-Y’-Z” Euler angle convention that is...

Consider the orthogonal coordinate system x = uv cosθ, y = uv sinθ, z = (u2...

Consider the orthogonal coordinate system x = uv cosθ, y = uv sinθ, z = (u2 −v2)/2, with u,v ≥ 0 and 0 ≤ θ < 2π. Express the volume element dV in terms of u, v, θ.

Define (x,y,θ) ~ P(x,y,θ) as follows: θ ~ Unif{0.1,0.9} (x,y) |θ ~ Bern(x|θ) Bern(y|θ) Where Bern(....

Define (x,y,θ) ~ P(x,y,θ) as follows: θ ~ Unif{0.1,0.9} (x,y) |θ ~ Bern(x|θ) Bern(y|θ) Where Bern(. | θ) is the p.m.f. for a Bernoulli random variable which takes the value 1 or 0 with probability, θ, (1-θ) respectively. Find probabilities a) Pr(x=0, y=0) ? (enter answer in decimal form, e.g. 0.56 ) (b) Pr(x=1, y=1) ? (enter answer in decimal form, e.g. 0.56 ) (c) Pr(x=1, y=0) ? (enter answer in decimal form, e.g. 0.56 ) (d) Pr(x=0, y=1) ?...

6) Define Z score and example of how it could be useful? 11. The scores on...

6) Define Z score and example of how it could be useful? 11. The scores on a Northwest Ohio High Schools ACT for juniors are approximately normal with mean 21.51 and standard deviation of 5.32. What are the first and third quartiles for the ACT Scores? 14) The Central Limit Theorem states that as sample size increases, the population distribution more closely approximates a __________distribution.

6. Let T (with pdf fT (.|θ)) be complete for θ ∈ Θ0 and suppose Θ0...

6. Let T (with pdf fT (.|θ)) be complete for θ ∈ Θ0 and suppose Θ0 ⊂ Θ1. Show that Let T is complete for θ ∈ Θ1. However, the converse is not true.

tow conducting cones (θ = π/10 and θ = π/6) of infinite extent are separated by...

tow conducting cones (θ = π/10 and θ = π/6) of infinite extent are separated by an infinitesimal gap at r = 0. If V(θ = π/10) = 0 and V(θ = π/6) = 50 V, find V and E between the cones. Solution:

Find the temperature distribution T(r,θ,z) inside a cylinder of height z= 20 and radius r= 8...

Find the temperature distribution T(r,θ,z) inside a cylinder of height z= 20 and radius r= 8 , if the cylinder temperature is zero in all surface except the bottom circular surface where it is divided two halves , the first is held at T1= 100 c and the other is held at T2=200 c. please use laplace equation and show me the solution with the details of the derivation .

A charge of -3.30nC is placed at the origin of an xy-coordinate system, and a charge...

A charge of -3.30nC is placed at the origin of an xy-coordinate system, and a charge of 2.5nC is placed on the axis at y=3.55cm. a) If a third charge, of 5 nC, is now placed at the point x=3.05cm, y=3.55cm find the x and y conponents of the total force exerted on this charge by the other two charges. b) Find the magnitude of this force c) Find the direction of this forces.

A charge q1 = 5.00nC is placed at the origin of an xy-coordinate system, and a...

A charge q1 = 5.00nC is placed at the origin of an xy-coordinate system, and a charge q2 = -4.50nC is placed on the positive x axis at x= 4.00cm . A) If a third charge q3 = 5.00nC is now placed at the point x= 4.00cm , y= 3.00cm find the x and ycomponents of the total force exerted on this charge by the other two charges. B) Find the magnitude and direction of this force.

A charge of -2.95 nC is placed at the origin of an xy-coordinate system, and a...

A charge of -2.95 nC is placed at the origin of an xy-coordinate system, and a charge of 2.20 nC is placed on the y axis at y = 3.85 cm . Part A If a third charge, of 5.00 nC , is now placed at the point x = 3.40 cm , y = 3.85 cm find the x and ycomponents of the total force exerted on this charge by the other two charges. Express answers numerically separated by...

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