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Conservation of Energy in Gravity

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data
    A boy at the top of a roller coaster falls through a vertical distance of 20m. What is the final speed of the boy if:
    a) His initial speed was 0
    b) His initial speed was 5 ms-1


    2. Relevant equations
    GPE at top = KE at bottom
    mgh = 1/2mv^2
    gh = 1/2v^2
    v = √2gh

    if the initial velocity (u) was not equal to zero, the maths becomes slightly different

    initial total energy = final total energy
    1/2mu^2 + mgh = 1/2mv^2

    therefore....

    v^2 = u^2 + 2gh


    3. The attempt at a solution

    a) 2x9.8x20 = 392

    b) 5^2 + 2x9.8x20 = 417


    The answers are:
    a) 19.8 ms-1
    b) 20.4 ms-1

    What on Earth am I doing wrong... what can I do... or what!?! D: I just don't understand!!!
     
  2. jcsd
  3. Oct 6, 2011 #2

    kuruman

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    Homework Helper
    Gold Member

    If v2=392 m2/s2, what is v?
     
  4. Oct 6, 2011 #3
    I love you and your wisdom. :D
    Thankyou so much, you've really made my day!
     
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