Chapter 17.1, Problem 1QC

If the vector field in Example 1c describes the velocity of a fluid and place a small cork in the plane at (2, 0), what path will it follow?

Example 1 Vector fields

Sketch representative vectors of the following vector fields.

a. F(x, y) = $\langle 0\text{, }x\rangle$ = xj (a shear field)

b. F(x, y) = $\langle 1-y^2\text{, }0\rangle$ = (1 − y²)i, for |y| ≤ 1(channel flow)

c. F(x, y) = $\langle -y\text{, }x\rangle$ = −yi + xj (a rotation field)