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 ) = 〈 0 , x 〉 = x j (a shear field) b. F( x, y ) = 〈 1 − y 2 , 0 〉 = (1 − y 2 ) i , for | y | ≤ 1(channel flow) c. F( x, y ) = 〈 − y , x 〉 = − y i + x j (a rotation field)
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 ) = 〈 0 , x 〉 = x j (a shear field) b. F( x, y ) = 〈 1 − y 2 , 0 〉 = (1 − y 2 ) i , for | y | ≤ 1(channel flow) c. F( x, y ) = 〈 − y , x 〉 = − y i + x j (a rotation field)
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) =
〈
0
,
x
〉
= xj (a shear field)
b. F(x, y) =
〈
1
−
y
2
,
0
〉
= (1 − y2)i, for |y| ≤ 1(channel flow)
c. F(x, y) =
〈
−
y
,
x
〉
= −yi + xj (a rotation field)
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Use undetermined coefficients to find the particular solution to
y"-2y-4y=3t+6
Yp(t) =
Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/s^2 until it reaches a speed of 60ft/s. Afterwards it maintains the speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 80 ft/s. Determine the distance traveled by Car A when they pass each other.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
Chapter 17 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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