alinakanus 3 years ago 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) =

1. shivam_bhalla

2. alinakanus

Let me get a screen shot, really quick.

3. alinakanus

4. alinakanus

The radius of the earth is given, 3960 mi.

5. shivam_bhalla

6. alinakanus

Why did you square root the denominator?

7. shivam_bhalla

Again typo mistake :p The square root is not present

8. alinakanus

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?

9. shivam_bhalla

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

10. shivam_bhalla

got it ??

11. alinakanus

That's for s as function of theta?

12. shivam_bhalla

$s = r \theta$

13. shivam_bhalla

Got this or I need to explain

14. alinakanus

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

15. shivam_bhalla

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

16. alinakanus

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

17. shivam_bhalla

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

18. alinakanus

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

19. shivam_bhalla

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

20. alinakanus

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?

21. shivam_bhalla

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

22. alinakanus

Oh! Got it. Got it.

23. shivam_bhalla

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

24. alinakanus

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

25. shivam_bhalla

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

26. alinakanus

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

27. shivam_bhalla

Welcome :D

28. shivam_bhalla

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

29. alinakanus

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

30. alinakanus

Thank you so much

31. shivam_bhalla

Welcome :)

32. alinakanus

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.

33. shivam_bhalla

@alinakanus , both the answers are right

34. shivam_bhalla

@alinakanus , both the answers are right

35. shivam_bhalla

@alinakanus , both the answers are right

36. alinakanus

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

37. alinakanus

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

38. shivam_bhalla

No problem. No need to apologise !

39. stan2244

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