A missile of mass 1 kg is launched with velocity $200$ m/s towards a tank of mass 50 tons moving towards it with velocity 20 m/s .
Find the momentum of the missile with respect to the tank .
My turn :-
$H(\text{missile w.r.t tank}) = H(\text{missile}) -H(\text{tank}) = 1\times 200 + 50000\times 20 = 10002000 \mathrm{kg} \cdot\mathrm m/\mathrm s$
Is the solution correct ?
In the inertial frame of the tank, the missile is traveling at $220\ m/s$ and has mass $1\ kg$, so its momentum (as seen by the tank) is $220\ kg$-$m/s$.
The tank is not at rest, of course, and that is why the relative velocity is $220\ m/s$.