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Homework Help: Finding distance -- Find the height of an object given ratio of two distances

  1. Jan 29, 2015 #1
    1. The problem statement, all variables and given/known data
    A body is dropped from certain height H. If the ratio of the distances travelled by it in (n-3) seconds to (n-3)rd second is 4:3, find H (take g= 10 m/s²) (answer: 125m)

    2. Relevant equations

    3. The attempt at a solution
    I did this way but I came to a dead end...
    To find H,
    s= 1/2 gt²
    = 1/2 * 10 * (n-3)²
    = 5*(n²-9)
    = 5n²+45.......(I)

    S nth = u+g/2(2n-1)
    = 5(2n-1)
    = 10n-5.....(II)
    equating (I) AND (2)
    5n²+45= 4
    ________ ___

    10n-5. 3

    => 3(5n²+45)=4(10n-5)
    => 15n²+135=40n-20
    => 15n²-40n=-20-135
    => 15n²-40n=-155
    => 15n²+155=40n
    => 15n²+155= 40

    This is a dead end....what should I do next...???
  2. jcsd
  3. Jan 29, 2015 #2


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    Education Advisor
    Gold Member

    The problem statement looks incomplete. What is n? Is n the number of seconds required to fall the distance H?

    Ok, you need to check your algebra a bit. (n-3)^2 is not (n^2 - 9). And 5 (n^2-9) is not 5n^2 + 45. And what are (I) and (II) and why should they be equal?

    Also, you need to be using the ratio you have been given. The distance in n-3 seconds is 4/3 the distance in the (n-3)rd second.
  4. Jan 29, 2015 #3
    Thanks...rechecking my algebra
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