Calculating Velocity of Mass in Ballistic Gel

[mpittma1]

Homework Statement

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. )

Homework Equations

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

The Attempt at a Solution

m(dv/dt) = kv²

mdv = kv^2dt

m∫dv/v² = 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, I am guessing i am making an algebraic mistake somewhere, any ideas where i should start?

 

[Chestermiller]

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