The position vector for a proton is initially
r = 8.0i -6.0j + 2.0k, and then later is
r = -3.0i + 6.0j + 2.0k, all in meters. What is the proton's displacement vector i-component?
j-component?
k-component?
To what plane is it parallel ('xy', 'xz', 'yz')?
The position vector for a proton is initially r = 8.0i -6.0j + 2.0k, and then...
1. 16 pts) The position r of an object in an xy plane varies as r (-sini+1-cos n) j. where r is in seconds and r in meters. (Set your calculators in radians for trig functions.) (a) What is the displacement vector of this object between 1-0 and 2n (b) What is the distance (or are length) travelled by this object between 1-0 and 2? Hint sin'e-(1/211-cos 200 (c) What are the object's speed and direction of motion at /6
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
A particle P with mass 5 kg has position vector r(r = 7.0 m) and velocity v(v = 5.0 m/s) as shown in the figure. It is acted on by force F(f = 8.0 N). All three vectors is in the xy plane. About the origin, what is the z-component of the angular momentum of the particle? About the origin, what is the z-component of the torque acting on the particle? About the origin, what is the z-component of the...
The position r of a particle moving in an xy plane is given by r = (4.00t^3 - 4.00t) i + (4.00 - 1.00t^4) j with r in meters and t in seconds. In unit-vector notation, calculate (a) r, (b) V, and (c) a for t = 2.00 s, (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the...
The position ModifyingAbove r With right-arrow of a particle
moving in an xy plane is given by ModifyingAbove r With right-arrow
equals left-parenthesis 4 t cubed minus 3 t right-parenthesis
ModifyingAbove i With caret plus left-parenthesis 6 minus 2 t
Superscript 4 Baseline right-parenthesis ModifyingAbove j With
caret with ModifyingAbove r With right-arrow in meters and t in
seconds.
In unit-vector notation, calculate
(a)ModifyingAbove r With right-arrow,
(b)v Overscript right-arrow EndScripts, and
(c)a Overscript right-arrow EndScripts for t = 2...
The position vector of a point which moves in the x-y plane is given by: r = (- 0.2 t4 + 1.8 t3 + 1.1 t2) i + (- 0.4 t4 - 1.2 t) j where r is in meters and t is in seconds. Determine the angle between the velocity v and the acceleration a when t = 1.7 sec.
1.
2.
3.
(a) In unit-vector notation, what is the sum of a - ! 3.4 m ji + 2.1 m |j and b-Ί-14.0 m i + 17.9 m |j . what are (b) the magnitude and (c) the direction of a + b (relative to i )? (a) Number Units (b) Number Units (c) Number Units The two vectors a and b in the figure have equal magnitudes of 11.9 m and the angles are θ,-30° and θ2-1060. Find...
What is the initial position vector i in unit-vector notation? 2m//cr ~---_., 4 m 3 m What is the final position vectorin unit-vector notation? 3 m 4 m What is the x component of displacement Δ r ? 2 m 4 m 3m5m ITm
Velocity in xy-Plane position in the xy plane is given by the vector (ct 4dtt)i +(2ct? -d')j, where c and d are positive c FInd the expression for the x-component of the velocity (for time t > 0) when the in the z-direction. You should express your answer in terms of the variables c and d. Find the n for the y component of the velocity (for timet 0) when the particle is moving in the y-direction. D
Force = 2.11 N i -3.19 N k acts on a pebble with position vector = 0.51 m j -2.12 m k relative to the origin. What is the resulting torque on the pebble about the origin? Enter i, j, and k component. What is the resulting torque on the pebble about the point (2.02 m, 0, -3.25 m)? Enter i, j, and k component.