A particle travelS along the circular path from A to B
in 1s. If it takeS...
A particle travelS along the circular path from A to B
in 1s. If it takeS 3S for it to go from A to C. Determine Its
average velocity when it goes from B to C.
Determine the parametric equations of the path of a particle
that travels the circle:
(x − 3)2 + (y − 2)2 = 4
on a time interval of 0≤t≤2π
A) if the particle makes one full circle starting at the point
(5,2) traveling counterclockwise.
x(t)=?, y(t)=?
B) if the particle makes one full circle starting at the point
(3,4) traveling clockwise.
x(t)=?, y(t)=?
C) if the particle makes one half of a circle starting at the
point (5,2) traveling clockwise....
One particle travels along the path
p1(t) = <2.666 cos(6.405t + 5.149) + 4.430, 2.666 sin(6.405t
+ 5.149) − 3.610, 11.18t + 6.633>
and another along the path
p2(t) = <1.084t + 3.125, 3.096t − 5.332, −2.925t +
4.377>.
The paths intersect at two points, one of which is a collision.
Find the point where the particles collide and the other point
where the paths intersect.
Let C be the closed path that travels from (0, 0) to (1, 1)
along y = x^2 , then from (1, 1) to (0, 2) along y = 2 − x^ 2 , and
finally in a straight line from (0, 2) to (0, 0). Evaluate Z C e
^3−x √ 3 − x ) dx + (5x − y √ y^2 + 2) dy
A particle of mass m orbits around the origin (0,0) in a
circular path of radius r.
(a) Write the classical Hamiltonian (energy) of this system in
terms of angular momentum of the particle.
(b) Write the Schrodinger equation for this system.
(c) Find the energy eigenvalues and their corresponding
(normalized) wavefunctions.
Particle A moves along an axis in the laboratory with velocity V
= 0.3c. Particle b moves with velocity of V = .9c along the
direction of motion of particle A.
What kinetic energy does the particle b measure for the particle
A?
A skater glides along a circular path of radius 7.40 m.
1-If he coasts around one half of the circle, find the magnitude
of the displacement vector.
2-What distance has the person skated?
3-If the skater coasts only around 73 degrees of the circle,
find the magnitude of his displacement vector.
4-What distance has he skated in this case? 5-What is the
magnitude of the displacement if he skates all the way around the
circle?
The path of a gymnast through space can be modeled as the path
of a particle at the gymnast's center of mass, as we will study in
a later chapter. The components of the displacement of a gymnast's
center of mass from the beginning to the end of a certain
trajectory are described by the equations xf = 0 + (10.3
m/s)(cos(18.5°))Tf 0.380 m = 0.640 m + (10.3 m/s)(sin(18.5°))Tf − 1
2 (9.80 m/s2)Tf2 where Tf is in seconds...
A small particle starts from rest from the origin of an
xy-coordinate system and travels in the xy-plane. Its acceleration
in the x-direction is 2m/s^2, and its acceleration in the
y-direction is 1m/s^2. What is the x-coordinate of the particle
when the y-coordinate is 12m?
Anatomy. Fully describe the entire path that water travels from
the root hair to the hydathode as guttation occurs. Correctly use
at least the following six anatomical terms in your description:
hydathode, stele, tracheid, trichome, vascular bundle, and xylem.
Note that you may need to use more terms than this to completely
describe this anatomical pathway.