Calculating Mass of Gas Needed to Correct Rocket's Course

[Maiia]

Homework Statement

A 6600 kg rocket traveling at 3500m/s is moving freely through space on a journey to the moon. The ground controllers find that the rocket has drifted off course and that it must change direction by 8.6 degrees if it is to hit the moon. By radio control, the rocket's engines are fired instantaneously (ie as a single pellet) in a direction perpendicular to that of the rocket's motion. The gases are expelled (ie the pellet) at a speed of 5400m/s (relative to the rocket). What mass of gas must be expelled to make the needed course correction?

I'm not really sure where to start with this problem...i assume b/c the velocity of the gases is perpendicular to the rocket, then its relative velocity is its actual velocity?

 

[LowlyPion]

It's a vector addition problem.

Except where you may have normally been thinking of Velocity or Acceleration as your vectors, this time it's momentum P.

You have the initial Vector direction of the Rocket given. And they made it simpler that they are going to do a 90° burn and you will have a new vector for your momentum corrected by 8.6° pointing at the moon orbital landing window, which if it misses may mean to ∞ and beyond.

So ...

$$\vec{P_c} = \vec{P_i} + \vec{P_{Burn}}$$

 

[steph.a]

What does Pc stand for in

$$\vec{P_c} = \vec{P_i} + \vec{P_{Burn}}$$

And what do you use as the final velocity of the rocket?

I'm really stuck on this one and don't know how to incorporate all the angles.