Question

The figures indicate that the higher the orbit of a satellite, the more of the earth the satellite can "see." Let θ, s, and h be as in the figure, and assume the earth is a sphere of radius 3960 miles.

(a) Express the angle θ as a function of h. (Remember to enter inverse trigonometric functions such as sin–1(x) as either asin(x) or arcsin(x).)
θ (h) =

(b) Express the distance s as a function of θ. (Remember to enter inverse trigonometric functions such as sin–1(x) as either asin(x) or arcsin(x).)
s (θ) =

Answer 1

figure please.

Answer 2

Let me get a screen shot, really quick.

Answer 3

The radius of the earth is given, 3960 mi.

Answer 4

r -->radius of earth.

Answer 5

Why did you square root the denominator?

Answer 6

Again typo mistake :p
The square root is not present

Answer 7

Ah, okay. That's actually what I got too, when I tried figuring it out now. Do you think you can help me with Part B?

Answer 8

ok

\[s = r \theta = r \cos^{-1} ({r \over r+h}) \]

Answer 9

got it ??

Answer 10

That's for s as function of theta?

Answer 11

\[s = r \theta\]

Answer 12

Got this or I need to explain

Answer 13

Can you explain a little bit? I'm a little confused. Is that for part b?

Answer 14

See I am little confused myself about s. I am assuming that they are taking s as arc length of a circle.

Answer 15

That's what I'm assuming too. But it's really confusing. I agree.

Answer 16

Do you want me to show you how to get s = r (theta) or continue to part C??

Answer 17

Can you show me how s=r(theta), please? Thank you so much.

Answer 18

See we know that

circumference of circle = 2(pi)(r)

If for
2(pi) angle ---> Arc length = 2(pi)(r)

Then
for

(theta) angle --> Arc length = 2(pi) (r) / 2(pi) * (theta)

Therefore Arc length = r * Theta

Answer 19

Oh, okay. I don't know why I couldn't get it in the first place. I was just overthinking it. Thanks! SO MUCH. Can we move on to Part C?

Answer 20

Part C is already done by me. Go above in this thread and check.

Answer 21

Oh! Got it. Got it.

Answer 22

Do you want me to do part d and part e or you will try by yourself??

Answer 23

I'll try by myself first. But can I check with you later to see if i'm correct?

Answer 24

Let me give you a hint because it is 4 am here and I am going to sleep now

Part d) Use s= function of h In this case , h is given. Find s

Part e) s= function of h. In this case , s is given. Find h

Answer 25

Oh, okay. THANK YOU SO MUCH! You saved my life. Haha. Good night!

Answer 26

Welcome :D

Answer 27

If you are having any doubt, post it here and I will see it tomorrow. :)

Answer 28

OK. I'll post what I got from the solving. And you can help me see if I did it right (:

Answer 29

Thank you so much

Answer 30

Welcome :)

Answer 31

Hey, when you get a chance, I computed for the answers. I got d) about 50,462.093 miles; and e) about 0.23 of a mile.

Answer 32

@alinakanus , both the answers are right

Answer 33

@alinakanus , both the answers are right

Answer 34

@alinakanus , both the answers are right

Answer 35

Ah, great! Thank you so much, @shivam_bhalla ! You really helped me a lot!

Answer 36

I apologize for the late response. I was in class up until now.

Answer 37

No problem. No need to apologise !

Answer 38

I still do not fully understand what the answers are after reading it over and over? Starting with A what exactly is the answer?