Question

In: Physics

A velocity vector field is given by F (x, y) = - i + xj a)...

A velocity vector field is given by F (x, y) = - i + xj

a) Draw this vector field.

b) Find parametric equations that describe the current lines in this field. c)

Obtain the current line which passes through point (2,0) at time t = 0 and represent it graphically. d)

Obtain the representation y = f(x) of the current line in part c).

Expert Solution

ANSWER:

Given that:-

A velocity vector filed is given by

(a) The vector field looks like

Flow lines looks like parabolas.

(b) By the definition of element lines, the target vector to these parametric curves at each point must equal to F i.e

(c) & (d) Intefrating we have

Passes through

so,

This is the required graphical representation of parabola.

genius_generous answered 2 years ago

Given the following vector force field, F, is conservative: F(x,y)=(2x2y4+x)i+(2x4y3+y)j, determine the work done subject to...

Given the following vector force field, F, is conservative: F(x,y)=(2x2y4+x)i+(2x4y3+y)j, determine the work done subject to the force while traveling along any piecewise smooth curve from (-2,1) to (-1,0)

Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x ,...

Verify the Divergence Theorem for the vector field F(x, y, z) = < y, x , z^2 > on the region E bounded by the planes y + z = 2, z = 0 and the cylinder x^2 + y^2 = 1. By Surface Integral: By Triple Integral:

Given a scalar fifield φ(x, y, z)=3x2-yz and a vector field F(x, y, z)=3xyz2+2xy3j-x2yzk. Find: (i)F.∇φ....

Given a scalar fifield φ(x, y, z)=3x2-yz and a vector field F(x, y, z)=3xyz2+2xy3j-x2yzk. Find: (i)F.∇φ. (ii)F×∇φ. (iii)∇(∇.F).

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )

Compute the derivative of the given vector field F. Evaluate the line integral of F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.

Let f(x,y) be a scalar function, and let F(x,y,z) be a vector field. Only one of...

Let f(x,y) be a scalar function, and let F(x,y,z) be a vector field. Only one of the following expressions is meaningful. Which one? a) grad f x div F b) div(curl(grad f)) c) div(div F) d) curl(div(grad f)) e) grad(curl F)

The flow of a vector field is F=(x-y)i+(x^2-y)j along the straight line C from the origin...

The flow of a vector field is F=(x-y)i+(x^2-y)j along the straight line C from the origin to the point (3/5, -4/5) A. Express the flow described above as a single variable integral. B. Then compute the flow using the expression found in part A. Please show all work.

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along...

Compute the line integral of the vector field F(x, y, z) = ⟨−y, x, z⟩ along the curve which is given by the intersection of the cylinder x 2 + y 2 = 4 and the plane x + y + z = 2 starting from the point (2, 0, 0) and ending at the point (0, 2, 0) with the counterclockwise orientation.

Question

A velocity vector field is given by F (x, y) = - i + xj a)...

Solutions

Expert Solution

Related Solutions