Rockets and Momentum?

Question

Here are the given:
Mass of Rocket = 5600 kg
Velocity of Rocket = 2900 m/s
Velocity of Gass Burst = 4300 m/s

The question says that a rocket is travelling toward the moon at the speed given above. To change the trajectory of the rocket, the engine fires a burst of gas perpindicular to the motion of the rocket at a speed given above.

What is the mass of the gas burst expelled? In kg.

Here is what I did (Used Conservation of Momentum)

(5600)*(2900) = [ (5600)*Vf rocket ]+ [ M gas burst * (4300) ]

I drew a diagram on an x, y axis, with the rocket initially moving all in the positive x direction with a velocity of 2900. Then I drew the gas velocity velctor of 4300, completely perpindicular (all in y direction). Using pythag. thm I solved for the magnitude of the total final velocity of the rocket. I got V f rocket = 5186.52
I plugged this value in, and found the final momentum of the rocket to be 2.90445e7. I then plugged and solved for M gas.
This didn't work, what am I missing?

Sorry the trajectory changed 11 degrees

Here is the question word for word:

A 5600 kg rocket traveling at 2900 m/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 much change direction by 11 degrees. By radio control the rocket's engines are fired instantaneously ( As a single pellet) in a direction perpindicular to that of the rocket's motion. The gases are expelled ( the pellet) at a speed of 4300 m/s (relative to the rocket). What mass of gas must be expelled to make the needeed course in correction. Answer in kg.

Answer 1

There appears to be a vital piece of information missing. You need to tell us by how much the trajectory changed!

So what if this burst of gas was fired? Presumably if different amounts of gas were fired PERPENDICULARLY at this speed (which is what you wrote), the rocket's trajectory would be affected by different ANGULAR amounts. For example, fire hardly any gas, very little directional change; fire a huge amount of gas, a huge directional change. So whatever angular change in trajectory occurs, it is clearly connected to the amount of gas fired.

Without ANY information on how much the trajectory is changed or how much it needed to change, you have given us ABSOLUTELY NO HANDLE on the amount of gas needed.

You also appear to have misused the conservation of momentum. The term on the LHS of your equation is the original FORWARD MOMENTUM, while the last term on the RHS is SIDEWAYS MOMENTUM, perpendicular to the forward momentum. It's just not clear what you're doing, or what YOU think you're doing.

Please re-read the question carefully, and make sure that you've given us all the information. Right now, it's IMPOSSIBLE to do this problem!

Live long and prosper.