The figures in these exercises show a horizontal layer of the vector field of a fluid in which the flow is parallel to the xy - plane at every point and is identical in each layer (i.e., is independent of z) . For each flow, state whether you believe that the curl is nonzero at the origin and explain your reasoning if you believe that it is nonzero, then state whether it points in the positive or negative z -direction.
The figures in these exercises show a horizontal layer of the vector field of a fluid in which the flow is parallel to the xy - plane at every point and is identical in each layer (i.e., is independent of z) . For each flow, state whether you believe that the curl is nonzero at the origin and explain your reasoning if you believe that it is nonzero, then state whether it points in the positive or negative z -direction.
The figures in these exercises show a horizontal layer of the vector field of a fluid in which the flow is parallel to the xy-plane at every point and is identical in each layer (i.e., is independent of z). For each flow, state whether you believe that the curl is nonzero at the origin and explain your reasoning if you believe that it is nonzero, then state whether it points in the positive or negative z-direction.
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.
You are on a rollercoaster, and the path of your body is modeled by a vector function r(t),
where t is in seconds, the units of distance are in feet, and t = 0 represents the start of the
ride. Assume the axes represent the standard cardinal directions and elevation (x is E/W, y
is N/S, z is height). Explain what the following would represent physically, being as specific
as possible. These are all common roller coaster shapes/behaviors and can be explained in
specific language with regard to units:
a. r(0)=r(120)
b. For 0 ≤ t ≤ 30, N(t) = 0
c. r'(30) = 120
d. For 60 ≤ t ≤ 64, k(t) =
40
and z is constant.
e.
For 100 ≤ t ≤ 102, your B begins by pointing toward positive z, and does one full
rotation in the normal (NB) plane while your T remains constant.
1.) is the quantity r(t+h)-r(t) a vector or a scalar? identify this object in the applet.
2.) is (r(t+h)-r(t))/h a vector or a scalar? Describe what represents r(t+h)-r(t)/h
3.) slide h toward to 0. How does r(t+h)-r(t) change? How about (r(t+h)-r(t))/h?
Describe geometrically what I does to each vector in the plane.
T(2) = [03] *
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Precalculus Enhanced with Graphing Utilities (7th Edition)
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