Answer
$a=133ft/s^2$, $a=200ft/s^2$
Work Step by Step
We know that
$\Sigma F=m\frac{dv}{dt}-v_{D/e}\frac{dm_e}{dt}$
$\implies 0=(w_f+w_{s_2})a-v_{D/e}\frac{dw}{dt}$
We plug in the known values to obtain:
$0=(2000+1000)a-8000(50)$
This simplifies to:
$a=133ft/s^2$
When the fuel runs out, we have
$0=m\frac{dv}{dt}-v_{D/e}\frac{dm_e}{dt}$
$\implies 0=w_{s_2}a-v_{D/e}\frac{dw}{dt}$
We plug in the known values to obtain:
$0=2000a-8000(50)$
This simplifies to:
$a=200ft/s^2$
