Maggie is moving in an xy-plane, with coordinates in meters. She
moves at the constant speed...
Maggie is moving in an xy-plane, with coordinates in meters. She
moves at the constant speed of of 6 meters per second.She starts at
the point (12,3) and heads toward the y axis along the line
y=1/3x-1.
A. Give Maggies parametric equations of motion.
B. Give an expression for the distance from Maggie's location to
the origin t second after she starts moving.
A
particle moves in a potential field V(r,z)=az/r, a is constant. Use
the cylindrical coordinates as...
A
particle moves in a potential field V(r,z)=az/r, a is constant. Use
the cylindrical coordinates as the general coordinates.
1)Determine the Lagrangian of this particle.
2)Calculate the generalized impulse.
3)Determine the Hamiltonian of this particle and the
Hamiltonian’s equations of motion.
4)Determine the conserved quatities of this system.
Sketch the curve y = x^2 + 5 , and the point (0,-6) on the
same...
Sketch the curve y = x^2 + 5 , and the point (0,-6) on the
same
coordinates. Find the equations of the lines that pass through the
point
(0,-6) and tangent to the curve y = x^2 +5 at the point x = a.
(Hint there
are two values of a : a > 0 and a < 0 )
(a) Find parametric equations for the line through
(2, 2, 6)
that is perpendicular to the...
(a) Find parametric equations for the line through
(2, 2, 6)
that is perpendicular to the plane
x − y + 3z = 7.
(Use the parameter t.)
(x(t), y(t), z(t)) =
(b) In what points does this line intersect the coordinate
planes?
xy-plane
(x, y, z) =
yz-plane
(x, y, z) =
xz-plane
(x, y, z) =
1. A plane passes through A(1, 2, 3), B(1, -1, 0) and
C(2, -3, -4). Determine...
1. A plane passes through A(1, 2, 3), B(1, -1, 0) and
C(2, -3, -4). Determine vector and parametric equations of
the plane. You must show and explain all steps for full marks. Use
AB and AC as your direction vectors and point A as your starting
(x,y,z) value.
2. Determine if the point (4,-2,0) lies in the plane with vector
equation (x, y, z) = (2, 0, -1) + s(4, -2, 1) + t(-3, -1,
2).