Answer
They must fire their engine for $317~seconds$
Work Step by Step
We can find the change in velocity:
$\Delta v = v_f-v_0 = (1.1\times 10^4~m/s)-(2.6\times 10^4~m/s) = -1.5\times 10^4~m/s$
We can use the magnitude of the change in velocity to find the magnitude of the change in momentum:
$\Delta p = m~\Delta v$
$\Delta p = (3800~kg)(1.5\times 10^4~m/s)$
$\Delta p = 5.7\times 10^7~kg~m/s$
The impulse exerted on the bird is equal to the bird's change in momentum:
$F~t = \Delta p$
$t = \frac{\Delta p}{F}$
$t = \frac{5.7\times 10^7~kg~m/s}{1.8\times 10^5~N}$
$t = 317~s$
They must fire their engine for $317~seconds$.
