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alinakanus

  • 4 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) =

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  1. shivam_bhalla
    • 4 years ago
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    figure please.

  2. alinakanus
    • 4 years ago
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    Let me get a screen shot, really quick.

  3. alinakanus
    • 4 years ago
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  4. alinakanus
    • 4 years ago
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    The radius of the earth is given, 3960 mi.

  5. shivam_bhalla
    • 4 years ago
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    r -->radius of earth.

  6. alinakanus
    • 4 years ago
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    Why did you square root the denominator?

  7. shivam_bhalla
    • 4 years ago
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    Again typo mistake :p The square root is not present

  8. alinakanus
    • 4 years ago
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    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
    • 4 years ago
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    ok \[s = r \theta = r \cos^{-1} ({r \over r+h}) \]

  10. shivam_bhalla
    • 4 years ago
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    got it ??

  11. alinakanus
    • 4 years ago
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    That's for s as function of theta?

  12. shivam_bhalla
    • 4 years ago
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    \[s = r \theta\]

  13. shivam_bhalla
    • 4 years ago
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    Got this or I need to explain

  14. alinakanus
    • 4 years ago
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    Can you explain a little bit? I'm a little confused. Is that for part b?

  15. shivam_bhalla
    • 4 years ago
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    See I am little confused myself about s. I am assuming that they are taking s as arc length of a circle.

  16. alinakanus
    • 4 years ago
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    That's what I'm assuming too. But it's really confusing. I agree.

  17. shivam_bhalla
    • 4 years ago
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    Do you want me to show you how to get s = r (theta) or continue to part C??

  18. alinakanus
    • 4 years ago
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    Can you show me how s=r(theta), please? Thank you so much.

  19. shivam_bhalla
    • 4 years ago
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    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
    • 4 years ago
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    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
    • 4 years ago
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    Part C is already done by me. Go above in this thread and check.

  22. alinakanus
    • 4 years ago
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    Oh! Got it. Got it.

  23. shivam_bhalla
    • 4 years ago
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    Do you want me to do part d and part e or you will try by yourself??

  24. alinakanus
    • 4 years ago
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    I'll try by myself first. But can I check with you later to see if i'm correct?

  25. shivam_bhalla
    • 4 years ago
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    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
    • 4 years ago
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    Oh, okay. THANK YOU SO MUCH! You saved my life. Haha. Good night!

  27. shivam_bhalla
    • 4 years ago
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    Welcome :D

  28. shivam_bhalla
    • 4 years ago
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    If you are having any doubt, post it here and I will see it tomorrow. :)

  29. alinakanus
    • 4 years ago
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    OK. I'll post what I got from the solving. And you can help me see if I did it right (:

  30. alinakanus
    • 4 years ago
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    Thank you so much

  31. shivam_bhalla
    • 4 years ago
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    Welcome :)

  32. alinakanus
    • 4 years ago
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    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
    • 4 years ago
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    @alinakanus , both the answers are right

  34. shivam_bhalla
    • 4 years ago
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    @alinakanus , both the answers are right

  35. shivam_bhalla
    • 4 years ago
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    @alinakanus , both the answers are right

  36. alinakanus
    • 4 years ago
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    Ah, great! Thank you so much, @shivam_bhalla ! You really helped me a lot!

  37. alinakanus
    • 4 years ago
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    I apologize for the late response. I was in class up until now.

  38. shivam_bhalla
    • 4 years ago
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    No problem. No need to apologise !

  39. stan2244
    • 2 years ago
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    I still do not fully understand what the answers are after reading it over and over? Starting with A what exactly is the answer?

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