# ballistics gel

**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, F_{net} = ma, a = dv/dt

**3. The attempt at a solution**

m(dv/dt) = kv^{2}

mdv = kv^2dt

m∫dv/v^{2} = k∫dt

m(-1/v(from v to v_{o}) = kt

m(-1/v + 1/v_{o}) = kt

(-1/v) + (1/v_{o}) = kt/m

(-1/v) = (kt/m) – (1/v_{o})

(1/v) = (1/v_{o}) – (kt/m)

v = 1/((1/v_{o})-(kt/m))

then after plugging in t = .0006 sec m = 0.015kg k = .08kg/m and v_{o} = 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?

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