Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v

Discussion in 'Calculator Requests' started by math_celebrity, Oct 24, 2018.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v

    1/2(2/5) = 1/5 since the 2's cancel
    r^2/r^2 = 1

    So we simplify, and get:
    mgh=1/2mv^2+1/5(mv^2) for v

    Divide each side by m, so m's cancel in each term on the left and right side:
    gh = 1/2v^2 + 1/5(v^2)

    Combine like terms for v^2 on the right side:
    1/2 + 1/5 = 7/10 from our fraction calculator

    So we have:
    gh = 7v^2/10

    Multiply each side by 10:
    10gh = 7v^2

    Now divide each side by 7
    10gh/7 = v^2

    Take the square root of each side:
    v = sqrt(10gh/7)

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