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Ballistics gel

  1. Mar 25, 2014 #1
    1. The problem statement, all variables and given/known data

    A bullet of mass = 0.015 kg is shot into a ballistics gel at 1200 m/s. The resistive force acting against the
    bullet is given by F = k v^2 where k is a constant = 0.08 kg/m.

    Find the velocity of the mass 0.0006 seconds after being fired into the gel. (250 m/s. )


    2. Relevant equations

    F = kv^2, Fnet = ma, a = dv/dt


    3. The attempt at a solution

    m(dv/dt) = kv2

    mdv = kv^2dt

    m∫dv/v2 = k∫dt

    m(-1/v(from v to vo) = kt

    m(-1/v + 1/vo) = kt

    (-1/v) + (1/vo) = kt/m

    (-1/v) = (kt/m) - (1/vo)

    (1/v) = (1/vo) - (kt/m)

    v = 1/((1/vo)-(kt/m))

    then after plugging in t = .0006 sec m = 0.015kg k = .08kg/m and vo = 1200m/s

    v(.0006) = -422.535

    which is not correct, im guessing i am making an algebraic mistake somewhere, any ideas where i should start?
     
  2. jcsd
  3. Mar 25, 2014 #2
    Your first equation should have a minus sign. The drag force is in the negative direction, and the acceleration is going to be negative.

    Chet
     
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