Please only answer part C Suppose r (t) = cos (pi t) i + sin(pi t) j + 2tk| repr
ID: 3108632 • Letter: P
Question
Please only answer part C
Suppose r (t) = cos (pi t) i + sin(pi t) j + 2tk| represents the position of a particle on a helix, where z| is the height of the particle. What is t| when the particle has height 8|? What is the velocity of the particle when its height is 8? When the particle has height 8| 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.Explanation / Answer
Answer :
Given that r(t) = < cos(t) , sin(t) , 2t >
The variable z represents the height.
So, we need 2t = 8 => t = 4.
(b) v(t) = r'(t) = <- sin(t), cos(t), 2>.
=> v(4) = <0, -, 2>.
(c) Since r(4) = <1, 0, 8>, and r'(4) = <0, -, 2>, the tangent line has equation
L(t) = <1, 0, 8> + t<0, -, 2> = <1, -t, 2t + 8>.