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(1 point) Suppose r() = cos(a) 1 + sin(at)j + 3tk represents the position of a p

ID: 2895661 • Letter: #

Question

(1 point) Suppose r() = cos(a) 1 + sin(at)j + 3tk represents the position of a particle on a helix, where z is the height of the particle (a) What is t when the particle has height 9? (b) What is the velocity of the particle when its height is 9? v (c) When the particle has height 9, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). Find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line. LC) =

Explanation / Answer

given r(t)=cos(t)i+sin(t)j +3tk

(a)

height is 9, z is height of particle

=>3t =9

=>t =3

(b)

velocity ,v=r'(t)

v=-sin(t)i+cos(t)j +3k

at height 9 , t=3

velocity ,v=-sin(3)i+cos(3)j +3k

velocity ,v=0i-j +3k

c)

r(3)=cos(3)i+sin(3)j +9k

r(3)=-i+0j +9k

vector parametric equation ,L(t)=(-i+0j +9k)+ (t-3)(0i-j +3k)