Question

Help! calculus 2.

Answer 1

I got a spiral for #1 and 480 hours for #2. I need help with 3 and 4

Answer 2

480 hours is how many days?

Answer 3

20days

Answer 4

total distance covered = \( \int_{0}^{??} \sqrt{r^2 + \frac{dr}{d\theta}} d\theta \) <-- looks like we have to find cycle first

Answer 5

edit *(dr/dQ)^2

Answer 6

R = 240 000 miles
dr/dt = 500 mph

time would simply be : R/(dr/dt)

Answer 7

480 hours. Thank you I need help with number 3 and 4

Answer 8

okay ... anything said about the orbit of moon?? elliptical or circular??

Answer 9

no but i think if you go with elliptical its way more complicated..

Answer 10

what do you wanna do??

Answer 11

I have no idea how to do number 3 and 4.... :(

Answer 12

circular or elliptical ... if it is circular, it will be simple. if elliptical it will be complicated.

Answer 13

yes

Answer 14

elliptical??

Answer 15

wouldnt it be too complicated?

Answer 16

let's try for circular first.

Answer 17

it must be something like r = k \( \theta \)

Answer 18

the period of moon is 27 days right?? we need to calculate angular velocity first.

\( \frac{d\theta}{dt} = \frac{2\pi}{27*24}\) <--- in hours

Answer 19

\( \theta = \frac{2\pi}{27*24} t\) <--- in hours

Answer 20

okay,

Answer 21

Also dr/dt = 500 mph => r = 500t

Answer 22

and find k?

Answer 23

k =162,000/pi

Answer 24

this is a parametric equation
r = 500 \(\theta\)/(2 pi/ 24 * 27)

Answer 25

sorry, it a polar equation ... of spiral

Answer 26

oh, yeah.. haha so r = 500 θ/(2 pi/ 24 * 27) would be the answer for #3?

Answer 27

http://www.wolframalpha.com/input/?i=polar+plot+%282pi%2F%2824*27%29+t+%2C+500+t%29

most likely

Answer 28

http://www.wolframalpha.com/input/?i=polar+plot+r+%3D+500+theta%2F%282pi%2F%2827*24%29%29+

Answer 29

Thank you very much, what about the total distance on #4?

Answer 30

in case our orbit is circular ...

Answer 31

okay ... for that, you have time right???
use that time to find \theta

Answer 32

put that value of \theta on the upper limit of the integral that i posted above.
and evaluate the limit ... that will give you the total distance.

Answer 33

what is \theta? just theta?

Answer 34

:'(

Answer 35

θ=2π/(27∗24) t

Answer 36

you know the t from second answer right??
use that t to find \theta and use it ...

Answer 37

I'm sorry, but i do not understand

Answer 38

θ=2π/(27∗24) * 480

Answer 39

evaluate this /// you will have the distance.