Chapter 11.2, Problem 32E

4. Let r(f) = ° 13 i - 6fj + Pk. (a) Find the unit tangent vector T(t) and T(3). | (b) Find the principal unit normal vector N(f) and N(3). (c) Find the tangential and normal components of acceleration, at and an for t = 3.

Q3: A particle traveling in a straight line is located at the point (1,-1,2) and has speed 2 at time t = 0. The particle moves toward the point (3, 0,3) with constant acceleration 2i+j+ k. Find its position vector r(t) at time t.

The position vector r describes the path of an object moving in the xy-plane. Position Vector Point r(t) = 6 cos ti + 6 sin tj (3V2, 3V2) (a) Find the velocity vector v(t), speed s(t), and acceleration vector a(t) of the object. v(t) = s(t) a(t) (b) Evaluate the velocity vector and acceleration vector of the object at the given point. E) - =

A particle traveling in a straight line is located at the point (1, -1, 2) and has speed 2 at time t = 0. The particle moves toward the point (3, 0, 3) with constant acceleration 2i + j + k. Find its position vector r(t) at time t.

Let f(x, y) = x64. Round the components of your answers to three decimal places. (a) At the point ( – 2, 1), find a unit vector in the direction of maximum rate of change. 7 i + i i (b) At the point ( – 2, 1), find a unit vector in the direction of minimum rate of change. 7 + i

How do you find the velocity and acceleration vectors at t=-1?

The vector describing a particular particle is given by T(t) = Rcos (wt)î + Rsin (wt) ĵ, where R and w are constants. (a) What is the magnitude of the position, |7|? What is its unit vector, f? (b) What is the velocity, ī, of this particle? What is it's magnitude, |0|? What is its unit vector, î? (c) What is the acceleration, a, of this particle? What is it's magnitude, Jā|? What is its unit vector, â? (d) Show that the acceleration points opposite to the position, ř° (i.e., â x -î), and determine the proportionality constant. |

(5) Cable AB exerts a 10 kN tension force on boom BC at point B. Express the tension force as vector and determine the angles which the tension force forms with +x-, +y-, and +z-axes. Ans: T = 4.061-7.61ĵ+5.07Â kN, = 0x 66.1°, 0, 139.5°, 0₂ = 59.5° = t 4 m T = 10 kN B 5 m 5 m 2.5 m

V(t)=?r(t)=?