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**silverstar45** A parachutist falls from a balloon at a height of y0 (=4000). k1 represents air resistance in stage one and k2 in stage 2. Air resistance is assumed proportional to velocity.

I've split this problem into two sections - free fall and after the parachute is deployed.

For the first section the initial conditions are v(0) = 0 and I have the formula

$\displaystyle v(t) = (mg/k)(e^[-k1t/m] - 1)$

and for stage two I have

$\displaystyle v(t) = (mg/k1)(e^[-k1td/m] - 1)(e^[(-k2/m)(t-td)]) + (mg/k2)(e^[(-k2/m)(t-td)] - 1)$

where td is the time of deploying the parachute.

I've integrated the first stage v(t) to find x(t), but I'm struggling to integrate the second stage. Please help.