Physics 11 Question

[Tomanomanous]

Ok, I'm stuck on this topic:

THE LAW OF CONSERVATION OF MOMENTUM states that, in any collision or
interaction between two or more objects in an isolated system, the total momentum
of the system will remain constant; that is, the total initial momentum will equal the
total final momentum:
Σpi = Σpf
or
m1u1 + m2u2 = m1v1 + m2v2


And the question is:

10 A small research rocket of mass 250 kg is launched
vertically as part of a weather study. It sends out
50 kg of burnt fuel and exhaust gases with a velocity
of 180 m s−1 in a 2 s initial acceleration period.
a What is the velocity of the rocket after this initial
acceleration?
b What upward force does this apply to the rocket?
c What is the net upward acceleration acting on the
rocket? (Use g = 10 m s−2 if required.)

[Lasercookie]

So you have a rocket that weighs 250kg. It releases 50kg of gas with a velocity of 180 m/s . This entire process takes two seconds. We want to find out what happens to the rocket after it releases this gas.

We know that momentum is always conserved in closed systems.
What's the net initial momentum? 0. Why? The rocket isn't moving before it launches. The gas hasn't been released yet, so that also isn't moving.

This makes find out the final momentum a lot easier. Let's set up our equation.


Now just rearrange for v_1.

So the rocket is moving at 36 m/s.

b. Impulse = change in momentum




c.
You could also do

[Tomanomanous]

oh my god, thank you!!! I officially love you!!!