# Bullet shot vertically up # # z'' = -g -af = -g -k*v^2 # with k = 1/m * 1/2 * A * c.w * rho coefficient.1(-1) -> -g # gravity coefficient.2 -> k # coefficient of friction coefficient.3(+1) -> v0 # initial vertical speed iintegrate (-g, 10*: friction) -> -v IC: v0 iintegrate (-v) -> z invert -v -> v multiply (-v, -v) -> v^2 cmultiply (k, v^2) -> kv^2 # make sure friction acts against the direction of propagation invert kv^2 -> -kv^2 compare v -> friction GT0: -kv^2 # v > 0 => moving upwards LT0: kv^2 # v < 0 => moving downwards output (v) -> out.x Output (friction) -> out.y output (z) -> out.z