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Babynini

  • one year ago

Falling Ball: When an object is allowed to fall freely near the surface of the earth, the gravitational pull is such that the object falls 16 ft in the first second, 48 ft in the next second, 80ft in the next second, and so on. a) Find the total distance a ball falls in 6seconds b) Find a formula for the total distance the ball falls in n seconds

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  1. Babynini
    • one year ago
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    @jtvatsim Whenever you're free! I'll try to work it out on my own until then :)

  2. jtvatsim
    • one year ago
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    Sounds good, be back. :)

  3. Babynini
    • one year ago
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    a_6=496feet

  4. Babynini
    • one year ago
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    ^ (part a)

  5. Babynini
    • one year ago
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    b) the formula would be a_n=16+(n-1)(32)

  6. Babynini
    • one year ago
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    Testing it with a_2 the formula seems to be correct :)

  7. anonymous
    • one year ago
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    I got the same thing for b, but 576 for a

  8. Babynini
    • one year ago
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    hmm let's see where I might've messed up a_6=16 +(6-1)(32) correct yeah?

  9. anonymous
    • one year ago
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    to find the 6th term, yes. But I think it's asking for the sum of the first 6 terms

  10. Babynini
    • one year ago
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    oooh, wow. I completely missed that.

  11. Babynini
    • one year ago
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    so i must find a_4 and a_5

  12. Babynini
    • one year ago
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    a_4=112, a_5 = 144

  13. anonymous
    • one year ago
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    for this one it's easy enough to do that, but there's a formula to find the sum of the first n terms.\[S _{n}=\frac{ n }{ 2 }(a _{1}+a _{n})\]

  14. Babynini
    • one year ago
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    oh o.0

  15. anonymous
    • one year ago
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    Yes those are right

  16. Babynini
    • one year ago
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    hm but I should probably use that formula you just used because the prof introduced it to us.

  17. Babynini
    • one year ago
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    a_6=176 correct?

  18. anonymous
    • one year ago
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    yes

  19. Babynini
    • one year ago
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    so we have s_6=(6/3)(16+176) =3(192) =576

  20. anonymous
    • one year ago
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    yep

  21. Babynini
    • one year ago
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    Fantastic! thank you so much :)

  22. anonymous
    • one year ago
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    you're welcome!

  23. Babynini
    • one year ago
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    oh wait! @peachpi the b) asks "TOTAL distance the ball falls at n seconds"

  24. Babynini
    • one year ago
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    my formula is not for the sum

  25. Babynini
    • one year ago
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    Right? So the formula would actually be s_n=(n/2)(16+a_n)

  26. anonymous
    • one year ago
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    right, and you'd so substitute the formula for the nth term for a_n

  27. anonymous
    • one year ago
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    If you need an explicit formula

  28. Babynini
    • one year ago
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    ok, it just asks for a formula that could generate any nth term.

  29. Babynini
    • one year ago
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    Er, should I put the formula to find a_n and also the formula for finding the sums?

  30. anonymous
    • one year ago
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    so I think what they're asking is for a formula where you would just stick in the n value and get the sum. Sn = 3(16 + a_n) but since we know a_n = 16+(n-1)(32) Sn = 3(16 + 16+(n-1)(32))

  31. anonymous
    • one year ago
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    does that make sense? can't really think of a right way to say it

  32. Babynini
    • one year ago
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    you mean sn=n/6(16+(n-1)(32)) (not ^3)

  33. Babynini
    • one year ago
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    ahh yes I see what you did.

  34. anonymous
    • one year ago
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    oh, yes. n/2

  35. Babynini
    • one year ago
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    ok :)

  36. Babynini
    • one year ago
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    thanks, phew. That was close. I almost put the wrong formula xP

  37. Babynini
    • one year ago
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    Sn = (n/2)(16 + 16+(n-1)(32)) is the final formula?

  38. anonymous
    • one year ago
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    yes. I mean you can do some algebra to make it prettier, but it's correct

  39. Babynini
    • one year ago
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    oh o.0 we should probably make it prettier.. hah

  40. Babynini
    • one year ago
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    sn=(n/2)(16+512(n-1)) is that still correct? and simplified enough?

  41. anonymous
    • one year ago
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    keep going until you get a quadratic, so distribute 512 and combine like terms

  42. anonymous
    • one year ago
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    wait no!

  43. anonymous
    • one year ago
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    |dw:1433989465521:dw|

  44. Babynini
    • one year ago
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    aiai too simplified we never did that in class hrm

  45. Babynini
    • one year ago
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    maybe up to the second thing you did

  46. Babynini
    • one year ago
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    (n/2)(32+(n-1)(32))

  47. Babynini
    • one year ago
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    does that work?

  48. anonymous
    • one year ago
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    yes

  49. Babynini
    • one year ago
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    ah ok. I think thats simplified enough o.0

  50. anonymous
    • one year ago
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    cool

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