Answer to Question #116790 in Calculus for Olivia

Question

Let v(t)=⟨5cos(t),5sin(t),3⟩. Then the length of v′(t) is
Select one:
a. √20

b. ⟨5sin(t),5cos(t),0⟩

c. 20

d. 25

e. √5


f. 5

Answer 1

We have:

$x(t)=5cost, y(t)=5sint, z(t)=3$

Then:

$L=\int \sqrt{(x'(t))^2+(y'(t))^2+(z'(t))^2}dt$

$x'(t)=-5sint, y'(t)=5cost, z'(t)=0$

Answer:

$L=\int \sqrt{25sin^2t+25cos^2t}dt=5\int dt=5t+c$