1 point) Suppose r(t) = cos(m)sin (m) j + 51k repre- sents the position of a par

Question

1 point) Suppose r(t) = cos(m)sin (m) j + 51k repre- sents 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 10? (b) What is the velocity of the particle when its height is 10? (c) When the particle has height 10, 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. (r) = Answer(s) submitted (incorrect)

Explanation / Answer

6)

(a)when height is 10

=>5t =10

=>t =2

(b)

r(t)=cos(t)i +sin(t)j +5tk

v(t)=r'(t)

v(t)=-sin(t)i +cos(t)j +5k

when height is 10

v(2)=-sin(2)i +cos(2)j +5k

v(2)=0i +j +5k

(c)

at t=2,point on curve is (cos(2),sin(2),(5*2)) =(1,0,10)

L(t)=<1,0,10>+t<0,,5>

L(t)=<1+0,0+t,10+5t>

L(t)=<1,t,10+5t>

L(t)=1i +t j +(10+5t)k

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